It's one of the biggest events on the Bemidji High School Athletic Schedule, the Rick Lee Lumberjack dual, 16 wrestling teams venturing to Bemidji to square off in the two-day dual format event. Crowd at venue all day long had to get a seat early. When we start with Brainer taking on Purim, Altie Danielson for the Warriors gets the near fall. He wins by decision 9-6. At 1-38, Kyle Pattonode working on the pin, he ends up getting it, but Purim wins the dual 52-16. Moving on to Pierce taking on the Tracy Panthers, Sebastian Warzeca gets the pin at 3-0-3. Pierce wins the dual by just five points. And the host Lumberjack's taking on Ottertail Central, Koi Olson kicking things off at 1-0-6. He's able to get the fall at 1-46. Later Seth Newby always a fourth to be reckoned with. The pin just a minute and 22 seconds in, Bemidji rolls the Bulldogs, 46-19, taking a look at the results after day one, Thief River Falls wins their pool, Detroit Lakes able to beat Bemidji to move on to the championship round, Brainer, they only suffer that one loss to Purim, they win their pool, and Frazy advancing via the tiebreaker in their pool. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


use and and i've also worked cross-party in collaboration on other things around violence against women and we have had successes in that so i'm hopeful that we will get success and that people get behind it because and you know for too long women have been let out of the state and that's why we invited you on to support you in your efforts um thank you very much for your time today pauline thank you greg take time uh take care sorry that is uh senator pauline oriley there the county's number one talk show the nine till noon show on highland radio the lotto jackpot is an estimated 2.5 million euro play responsibly in store in app or at lovry.ie the national lottery it could be you attention graduates it's time to celebrate your incredible achievements at the tastiest place in town backstage bar and grill whether you are celebrating with a small group or hosting a grand party backstage bar and grill has the perfect space for you call now on 07491 21976 to make a reservation tickets get your tickets Arsenal Chelsea Leeds Liverpool Manchester United Spurs and more bottom games at all the gold score don't be shy it only takes a minute to win it it's cabri FC's biggest football ticket giveaway ever plus thousands of other prizes to be won every game week just head to match the minute dot cabri FC.com to get your match minute if a goal scored in that minute you win enter today season sees apply show the monday blues the door kick them into touch banish them for good with a wheat treat at kelly's diner in neverkenny maybe a coffee and scone or an all-day breakfast or a burger and chip with american-style booth seating fast and friendly service a menu packed with tasty choices at great value and loads of parking it's a great stop off any day of the week take back your monday's at kelly's diner mountaintop at a kenny oil local enterprise office dunningall invites you to come along to its meet the makers craft showcase in law s castle on friday the 20th of october from 5 30 come and celebrate our local craft businesses explore a wide range of unique gifts and meet over 40 talented makers behind dunningall's finest crafts register via local enterprise dot ie forward slash dunningall or email info at leo dot dunningall coco dot ie for more information highland radio time checks with expressway travel route 32 from letter kennedy doblin when you book online and travel for less expressway bringing you the time art the time now is 11 23 now as we were discussing on the program um the night before last uh two boss loads or two bosses arrived into boncrana with her at the figure of 66 uh mostly many if not all men uh presumably asylum seekers international protection uh candidates and they moved into accommodation in boncrana which is generally accepted is free to a room and there's different views on this and we're going to hear both sides of it now gareth good morning to you we'll go with you first how are you getting on yeah not too bad great so what's your reaction not it's our pleasure what's your reaction to the reaction to the arrival of these men in boncrana i i tend to question things so there's lots of things that have been said uh by individuals in that protest but i'm not sure where they're getting their information from obviously people came on yesterday and said what is vetted and what is on vetted i guess if these guys are under a an asylum seeker program they are either in the process of being vetted or vetted so the concern that the that the protesters have may be unwarranted um i how much information the general public need to be given on individuals coming into their country is i guess the question that i would have i mean my neighbors i don't know their criminal background i don't know you know i've met i've you know i'll say hello to them i'll get to know them but i don't know their criminal background and i don't know where they come from so i don't think the general public need to know the background of everyone coming into their area but gareth do you think they could have an interest in the fact that these people are from different areas they don't know each other uh necessarily they may do they may not um and that they are all being put into this accommodation and arguably there aren't the services around them to support them activities to entertain them uh capacity in the health service for them if they require it do you not see that maybe even that element of it might cause some concern yeah i appreciate that um and i uh a few months ago there was a firework launched at one of these accommodations uh and a response that i had as a person of the general public i didn't know was to well what can we do to get to know these people to find out who they are you know sit down and listen to their story and and the response that myself my wife did for that was we know that there is what's called an intercultural cafe in boncrana that's an opportunity for locals to uh get to know some of these refugees and the science he was coming into the town it's between 11 a.m. and 1 p.m. uh in yes on Thursday um what did you learn from it we learned that these you know we learned some of the stories of some of these people coming in and they come from all parts of the world and not just new korean but africa south america and the middle east and uh they they they have come from traumatic experiences uh i mean these men that came to boncrana monday obviously they're asylum seekers they're they're taking asylum from something um and uh well that has to be evaluated obviously garth with which is what the yeah the process is all about but you know like regardless of where they're from skin color whatever do you not understand or would you understand that maybe people that maybe you know women or women with you know or parents with children or what have you might have a natural inbuilt caution now in walking past accommodation that now has you know 66 odd men uh i don't mean they're odd i mean the number i don't know the number sorry i'll rephrase that strike that 66 men approximately um who you don't know the background of it's it's an unusual situation to have 66 people that you have no knowledge of in one area can you understand how people in that area might be now cautious that there could be a threat it's a perceived threat there's no evidence to suggest and in fact i contacted the guard on this on regular occasions in dunagore whatever about anywhere else the arrival of refugees or international protection candidates has not seen any increase uh or spike so often it is perceived you know there's lots of violence that goes on and it ain't it ain't uh these guys that are involved in it for the most part right that's what the guard he tells us but could you understand how there can be a perception that it's now more dangerous and that the the community has changed and there's fear there oh yeah sure there's uh perception and and fear comes from the unknown and the best way to uh to combat that is to get informed um but sure if if if uh that's a single uh mom walking her kids past that building is you know uneasy well i uh i can understand that but uh you know in this day and age i think as parents and i i have a child in a school in a school in bunkrana and we just need to be aware of everyone around us okay and just to be clear uh gareth because someone might text in if you lived immediately beside this property you would have no extra concerns than you have right now with the arrival of these people okay that's your view gareth thanks i would i would introduce myself get to know them okay and uh and get informed all right gareth thank you very much indeed that's gareth's view uh david you're listening to gareth there what's your opinion well my opinion greg is that um first out everybody's saying that uh there was a man on yesterday day saying that these are lovely people and all that you get to know them and all that the people on that bus the other nights were given slipping us the bird giving us the finger of the bus like they're they weren't being nice and being afraid of coming in they were looking to get asked the bus even though there was a hundred not merely 200 people there telling them not to get asked of us there was apart from that apart from being unverted it's unverted as an issue but 66 men doesn't matter what nationality they are if you stick them into the baldin not giving them work not giving them anything to do they're going to get bored they're going to start falling out with the local community no matter what way you put it there's always if you take 66 men from doblin or from cork or stain or anywhere it's going to be the same David have we seen have we seen that though because you know there's a there's a pathway presumably for them to get I know that Dave listen I'm going to respect David I'm going to respect you and listen to what you have to say but if you just listen to the questions as well and we can get to the bottom of it I mean that with absolute respect David but you know there is a pathway then for them to become integrated in the community is there not maybe there are job vacancies in the area or work that they can do does that not take time it doesn't happen on night one you know them coming in on a bus in the middle of the night yes it looks terrible yes maybe some of them flick the bird because they saw a lot of people saying go home we'll get out of here right so once we get past that do we not have to wait and see if it works or are you convinced that it can't work I can't work because there there isn't work in the local community for the locals never mind we'd like any shown alone is lost over 600 people on the the age of 25 that's since Christmas like young ones going away to Australia America or whatever early as there was work here them young ones would not be going like so why are they bringing 66 men and when there is no work in our area for them they're just isn't like there's no industry there's no factories there's no nothing for them people to go to work on so what are they going to do they're going to sit on it and basically an army barracks or a prison is basically what they're going to say they shouldn't be bored and obviously they're not going to be starting smoking inside so you have 10 or 20 and smoke they're going to be standing outside the whole time smoking David that's going to be on easy for anybody walking up and down like you know I mean we can dispute whether or not they're economic migrants or the fleeing whatever okay but listen we've seen what's happening in Gaza at the moment and other parts of the world okay from a human perspective you know a fellow human beings perspective because they are actual human beings just like you are and like I am do we not have a role to offer them protection to give them a chance at life do we not have a responsibility I think Ireland has done enough to be honest with you at what point in this country do we say the hotels hope like we're ticking and people there's people in Bunkrana at the minute with their houses having to be demolished by Jamaica and they can't get another house to rent to move on to they can't like I was talking to people this morning that cannot get another house to move on to their house is scheduled for demolition and they cannot get another house to move on to they asked me did I know of anybody with a field that would rent them a field so they could put a mobile home into the field that's how desperate the people of Bunkrana have become all right stay there the owners of this building what's the top the owners of this building converting it into six nice big apartments and renting it out to people that had made it now it's all about money that's that's pure and utter greed is what this is about stay there David um Sinead Stewart is a member of Bunkrana for all Sinead can I start with do you at least understand or respect people's concerns with this development and how it was done Sinead thank you Greg good morning thanks for asking me on um yeah um look I just firstly want to say I absolutely take on board people's concerns when it comes to resources and things like that um this is something that I think everybody can agree on is that the resources that Donnie Gull gets and and he's shown is the it's the precaution of Donnie Gull never mind and Donnie Gull's the forgotten county so everybody everybody can can agree on that that is absolutely not in question um what I suppose and what I don't agree with and I suppose the group doesn't agree with is that there is there's a judgment being passed on people coming to the town before they have even arrived into the town and it only unfortunately seems to be one or two sort of sections of of um people who are presumed guilty of some of the you know when you hear some of the the rhetoric and stuff like that and to be clear I am not saying that everybody who's without that protest or everybody you know um that was you know has concerns about this is employing that rhetoric or agree with that and I said it yesterday if we park the project fear stuff that in other words people people are going to come and drag you out of the house and do this that and then right because uh like there is an awful lot of uh crime against children in this country and has been historically we have uh almost 200 000 children living in poverty our child protection record in this country is crap uh we are screaming out for foster carers we're screaming out for families to adopt children that have been abandoned abused and misused our figures in terms of the abuse of women the rape of women and what have you they're terrible they're already there and I think we should also focus our anger on actually sorting that out rather than a perceived threat from people coming in that being said Sinead that being said people are concerned at the potential for it we have no idea of their background we have no idea where they're where they've come from what they have done in their past they maybe they've done nothing but no one's given this information we had it yesterday from Dez some of them don't have passports so you can't really you can't give them an interview but you can't really check what their background is and what have you so that is going to cause fear and people are going to be afraid of I kind of knew my community I knew who to avoid I know where I live people with a bit of a reputation right and that you avoid or there's some bad in them right but this is a whole group new group of people that people don't know the background from can you criticize people for thinking is that a potential this or is that a potential that Sinead really can you I can't I can't criticize people first for wondering is it a potential and thinking in terms of safety but as we can see and I mean it was very much highlighted on the program there Greg about the with with we Karen Harkin no we we don't always know exactly what's going on we absolutely do not always know what's going on this is happening and we don't always know who to avoid in the in the time um you know this is this is something that happened across the world if we are doing a national approach Sinead we need to surely review how we're doing this in terms of listening to the public addressing their concerns we can still meet our international obligations but do do this correctly not move people around in the cover of darkness because it's better to ask for forgiveness than permission and that's precisely what the policy is and that's terrible and I absolutely agree with you on that that is an absolutely horrible horrible way to be doing it the only thing I would say to you right is that so I'm sure you remember whenever we we formed the the welcome committee for people who were coming to my vote right and there was a meeting there and you know there was public there was public meetings and things like that a few days later what happened the place was burned to the ground so I don't know you know and that was the first time that anywhere was burned to you know any potential asylum seekers or people seeking refuge any accommodation like that that's not reflective that's not reflective of that that action of an individual we can't say he's reflective of the the wider community the concerns and I spoke to him where the fact that some people couldn't get their children into school they couldn't get boss places they couldn't get a booking at a GP that was really what I heard from people not the extreme views whereby it would drive someone but listen we're gonna have to come back to this because it is is so important Shade I really appreciate your time great do you want to say yeah very very finally what I want to say is look um I think we all need to be talking I think we everybody needs to be talking together as a community right but I also want to make sure that anybody who has come to the town anybody who has been in the town um you know anybody who especially the residents and the likes of the sailors rest or anybody who's come from Ukraine or anywhere like that please please know that the you know the vast majority of people in Moncran are not outstanding at a protest stopping you from coming in and saying that you're not wanted we absolutely want you to hear you're more than welcome and I just want to make sure that everybody who has come to the town knows that okay Shade and I get what you're saying but also I have to acknowledge that just because people didn't stand on the street it doesn't mean they're not sitting in the front rooms having conversations as well and everybody everybody needs to be heard okay thank you very much indeed within reason obviously you understand what I'm saying Shade thank you very much indeed uh David um listen you've been heard I think you know the only way we're going to get anywhere David is we all as a community come not we as a community come together and discuss this in the in the way we're doing now uh one thing briefly David go ahead yes Lik Shinai's making out there that like we're a racist or whatever I'm not accepting that I'm not accepting that at the at the at the protest we had Polish we had Slovakians we had Romanian there was Germans I guess it's not just the I guess that's not been said on this yeah that has not been said on this program and Shade never said that I understand but I'm just saying but I don't want to get into that I don't want to get into the right wing left wing racist not racist stuff I'm not doing it because we're not because what happens then is we can't have the convolt and we need to have the conversation David you need to be able to come on and Shade and Kim yesterday and Des and we need to be able to speak together and we don't have to call each other's names and I know the majority of people were not motivated by by race and and that's been very well reflected over the last couple of days and that's the way I want to keep it Dave and I appreciate your time today are you happy enough okay take care David bye bye bye bye okay back with more after these watch the show live now on youtube facebook and at highlandradio.com at AXA we know running a home can run up your costs too that's why you can save up to 30% on our home insurance get a quote today together we've got this AXA know you can policy terms and conditions apply minimum premium is 160 euro a 30% discount is available after three consecutive years claims free 15% after two consecutive years and 10% after one year claims free AXA insurance stack is regulated by the central bank of Ireland enhance your skills with CFTECH's part funded training programs at CFTECH we provide courses including first aid roadworks people moving and handling confined spaces electrophusion and machinery training for Ireland and UK sites also online programs such as water hygiene construction supervisors safety reps and much 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let grow letter candy or online at tinnies toys dot com lay down join highland radios outside broadcast team this thursday afternoon from 240 in the letter candy credit union for their final card draw of the year two lucky letter candy credit union members will each win a brand new Toyota Yaris cross a number of cash prizes will also be given away so tune in this thursday from 240 to hear if you're a winner with letter candy credit union Hickey clark and langan insurance brokers in letter candy are recruiting for an insurance advisor to join the team candidates can have a leaving certificate or relevant third level qualification or be qualified to approved product advisor or certified insurance practitioner standard apply with an up-to-date cv for a media consideration by emailing chevon at hcl.ie Hickey clark and langan general insurance brokers trading as Hickey clark and langan are regulated by the central bank of ireland business matters in association with the faculty of business at atu dunnegall for a career in financial governance consider the level nine ma in governance and it in financial services starting in january contact the exact ed coordinator on 91 86 206 or email donald.hanigan at atu.ie today okay carol donnell good morning to you good morning great good to have you on the program we're looking forward to the business matters podcast which is live right now on our website but let's catch up on some news first because we are tight for time leo support clinic tell us about this the big all local enterprise office will hold this next business support clinic in boncran on friday week as october 27 from 10 a.m. to 11 a.m. those who attend the event will find out more about the enterprise reports that exist and how they may help to develop a business all right the sustainable conference system sustainability conference could turn out yeah sustainability for business stroke green skill is for success it was a conference held by the larkinny chamber of commerce and association with tech northwest skillnet and was held at the tcs campus down below us here last thursday morning greg approved a big success over 40 businesses and attendants so the event was organized to stimulate interest in the sustainability issues which obviously are big issues at the moment and how they are impacting business locally business owners heard contributions from a number of industry experts who talked about their experiences and the various stages of progress they're making on their sustainable journeys really interesting and it's an issue that's going to be a bigger player for businesses as we go forward all right talk to me about the larentic forum yeah just caught this yesterday the this year's larentic forum which will have the overarching theme of sustainable coastal communities will take place at the atc campus in kelly bags next month the three-day hybrid conference will be held from tuesday november the 7th to thursday november the 9th the first day we'll look at sustainable tourism and the creative economy with the second and third days focusing on the blue economy within the partner regions and for more and for that greg log on to larentic forum dot com larentics about isn't it yep i think the cannons up in one of the cannons is up in downings is that it is the larentics i think so yeah yeah um the enterprise awards for the seard yeah they'll be on coming around greg applications are now open for local enterprise office donnie gall enterprise awards for 2023 so with 11 categories and a prize fund of 14 000 euro this is a good opportunity for local businesses to get recognition for their achievements over the year the closing date for entries greg is monday october 23rd at 12 noon and to enter and find out more about the awards check out donnie gall local enterprise office his social media platforms and if you want to own a garden station yeah uh for former garden station gurur will be sold at a live stream property auction on friday november the 3rd the station at bumbeg has a reserve price of 30 000 euro and the sale has been attracting plenty of attention over the last week the building which comes with its own holding cell is being auctioned by estate agents oh donlan anguish let's say it could tell some stories are we just thinking that yeah indeed all right let's talk exactly right you guessed on this week's podcast gear my guest this week greg is the owner of the station house and letter kenny brian galler brian began to explore the possibility of building a hotel on the family site along old town road in 2002 construction began in september 2005 and the 81 bedroom hotel opened its doors on august the first 2006 built by local contractors by the construction the station house hotel employs a team of 50 people in this clip greg brian talks about coming up with the idea to build a hotel on the well-owned site at the bottom of the town back in the early 2000s we thought on various things maybe some retail apartments and we figured then though there were enough apartments in the lower main street that maybe maybe a hotel there was an urban renewal scheme on shortly before that or around that time and i remember being at a meeting and there was some talk about tax reliefs for hotels that there were a hundred percent tax relief on hotels so i went away i'd done a bit of homework i approached my accountant pat keaton uh steward mclaughlin uh i thought i said i was thinking i'm building a hotel pat says right i don't know what i thought but i says that's in my head anyway pat uh he always says well you need to get a business plan done so there were a young man at that stage he was lecturing in business and market and billy bennett and he said if you go to billy billy might do a business plan that's the fourth thing you'll need so i approached billy and uh i said billy we're thinking on bolton hotel we need a business plan i do feel it would work all right brian gallagher there now the full interview with brian is available for right now for you right now to stream or download from our website hallandradio.com wherever you get your podcasts providing its Spotify right tunes and business matters is broadcast this sunday evening after the six o'clock news kiran but it is the last one with you at the helm first greg well what give me a mind here uh move it on greg after three and a half very good years and that listen has been a great experience how many podcasts 167 wow apart from one what i wasn't in great form uh over christmas 2020 when i had the the covid well that's because he had covid ten times john brison uh stood on but look at was uh look i always had a passion understand business greg but i learned so much uh about an area that i didn't really know a whole lot about um the people that i went that were very welcoming and uh i would like to think that when when the when the podcast started it as well somebody asked me what that i wanted to be and i said i would like it to be a friend to businesses and i would like to think that i hope that that that might be the case yeah for sure no doubt about it and there's a fantastic archive of stuff that you can always reflect on and best of luck with your future endeavours which includes a marathon yeah which is not why you stopped so thanks for that opportunity greg um there are 20 members from that academy athletic club um taken part in two marathons uh on the last sunday in october there are 16 of us going to dublin and there are four going to frankfurt and collectively we are raising money for the irish moral neuron disease association uh there's a member of our of our own club uh that is living with moral neurons at the moment uh we'll be thinking about him and uh anybody that they have any donation big or small there's a go for me page there we'd appreciate any donation all right karen thank you very much indeed and thank you for uh the production of a brilliant podcast and as i say uh we're gonna miss you coming in on a wednesday but thank you well not for the same i'll still be program ready to get into the carousel come up here for a week well don't right thanks karen thanks greg um now business uh matters takes a short siesta and uh we'll return in the not too distant future but again thank you so much to karen on donal for uh all of his endeavors over the last 167 episodes okay we are all right karen it's goodbye now i've got more important guests he doesn't want to go right okay we have uh for young people in studio with us uh we have students and the principal of st saffins national school uh castle fin all in situ and we'll just move this slightly that way so i can hear you um tracer mcbride do you want to introduce our guests uh to us greg uh here beside you today you have james mcgranahan and ethan shovelin all pupils of st saffins national school thank you so much guys uh ethan where are you which one are you ethan well you're gonna have to speak up a bit ethan okay uh how are you getting on okay now why are you in here ethan tell you about the tractor okay and what's happening um tractors there'll be tractors lorries and trucks and vintage cars just you move back slightly go on so i can hear you that's it good lad and there'll be like rally cars and motorbikes and stuff and there'll be a craft fair with 25 stalls and there'll be celling jewellery candles you can sit down and try celling cars and clothes okay are you looking forward to it all right okay do you like tractors yeah classic cars really okay that's fine i won't give you my one then uh ethan where are you no that was ethan that was ethan sorry i beg your pardon owen yeah come on owen now you uh look the part here i love your caps tell us about your cap well i've got this cap for christmas last year and just you haven't took it off since now we can't see on the camera or hear on the radio but you've got a fine pair of boots and you talked to me about them not normal school where i would say no you got to wear them especially for today right tell us what are you looking forward to about the tractor run and craft fair on sunday well i'm mostly looking forward to just the tractor run yeah getting around and well do you have a favorite tractor yeah what is it new holands new holands all right what who and what colors that blue oh i know the ones now they're big that's that your dreams have one of them yeah and what about any old vintage tractors have you any interest in them now one three five now uh flow your hat off wouldn't it without the cap on well forward forwards okay i have to be careful what i say you've been just now because i can end up getting in trouble i have to be really careful okay uh james my gran han are you excited for sunday yes what do you like about what are you looking forward to most i'm looking forward to most the run itself and the music by kenny crawford and the best dressed dog and pumpkin caravan pumpkin caravan that's a mess i have a pumpkin at home and i don't even know where to start probably take the top off it but i'm looking forward to it maybe bring it with me uh so we're talking about this weekend it's a tractor running craft fair taking place on sunday tractor registration from 11 a.m with the run commencing at 12 30 p.m there's going to be tractors trucks lary's bikes vintage and modified cars and all welcome to join in the run with proceeds going to the donagall hospice and saint saffron's uh national school and as you said they're uh james live music on the day as well yeah all right okay and you're looking forward to the tractor to you in one or are you just going to be watching i'm going to be in one oh do you know which one it is yes i'm going to be in a saloon with my grounded oh fantastic brilliant okay and he's going to have to wash it all day south of each other since there's no point landing with it filthy all right and are you interested in the classic cars or the tractor or the lary's or not really these are all tractor boys aren't you it's okay uh tracy it's going to be a great day isn't it and uh raising funds for the school which is fantastic tell us a little bit about the school and don't go hospice we'll talk about the school first yeah so um we're situated just outside um castle fun gregg we're in a quite rural area so i suppose um this is our second tractor on and we've had our first one was a huge success with over 300 tractors and um i suppose we were looking to raise money this year to put an outdoor classroom to onto the school grounds and uh we said why not run a tractor run again but this year we decided to share our profits with the donagall hospice so um we've had unbelievable support um not just from our parents we've had amazing support from community volunteers from the cpa center where it's been held and people who aren't even associated with the school you know there's a great sense of community spirit and castle fun um garth porter has and his brother andrew have given us their yard as well because we need more space um so between steve and kennedy and the cpa and garth um and his brother andrew with their their own ground their own farm and grounds they've been very supportive of us and i suppose it's just a testament to the community as well you know and it's a real community day out so whether people have tractors or trucks or bikes or whatnot or they don't and they're just coming you know this there will be a great um i suppose interest there for for families in general for them i love tractor runs i love them especially when you've got lorries and trucks and everything else involved yeah um and owens owens coming in are really amazing it's it's we didn't even tell you about this but owens coming in and not a tractor right what is it owen well it's a bread van with the black took an off of it and the cattle body put on it oh wow remodeled bread vans right well this is one of the modified yolks right uh lads anyone anyone do you want to say hello to anything you want to say ethan um i want to say hello to our teacher must have fallen okay right and you're asking him no homework is that it is that what you said no i'm gonna hurt that all right owen um i'd like to say hello to my mom and my granny excellent i'm not only the listener i'm sure they're watching you too very very proud of you uh owen what about you james i would like to say hello to my mother and father and my granny and who did you hear yourself because it is perfect there's not an error at a place my my father did it well i think he deserves an award okay listen have a fantastic day on sunday will yous yeah all right and enjoyed and tracy thank you very much yeah they have a wee present for you here right too actually okay is it a hat give it to me over here quickly so stick it on we have to go what does it say say this is now it'll keep you warm for the winter that's it you see the thing about me is when you give me a present i actually use it i've got a cop that was given to me about six years ago and i still use it uh every single day this hat now is part of my wardrobe thank you so very much have a great day sunday thank you all right thank you so much indeed to eth and owen james and last but not least uh tracy uh students and principal of st saffins national school in castelfin they're looking to raise money to develop the school it's a weekend tractor and tractor on a craft fair it's taking place on sunday october 22nd register your vehicles from 11 a.m it starts at 12 30 p.m if you're not in it get out and enjoy it uh it's going to be a fantastic day as i say and also supporting donogall hospice there's going to be live music fancy dress a pumpkin carving competition what a way to spend your sunday free refreshments also for all drivers and free entry for the general uh public okay uh on sunday to drive a tractor no problem i've got it on my license i got my license that long ago i'll see what time it is and if i can squeeze it in and get plan information all right listen thank you all very much uh we're going to be going a little bit late to the news but you know what it's for a good cause see you tomorrow


Okay, in the last class, we started talking about this hypothesis testing right, we introduced what is hypothesis testing and we defined what is a rejection set, we talked about various types of error, particularly we talked about type 1 error, type 2 error and we defined type 1 and type 2 error using your power functions, okay and then discussed what should be the ideal hypothesis should look like in terms of its properties for power function, okay. And then we discussed some examples, especially about this binomial case and the Gaussian case so, what we will do today is little bit discuss this example more. So, we said okay let us say we have a sample coming from a binomial distribution which has parameter phi and theta, we could equivalently think of these are like a phi samples coming from a Bernoulli random variable with parameter theta, but here I am just taking one sample coming from a binomial which I could. Now, we want to check whether the theta is taking value less than half or it is taking value more than half, we have to decide a test here.  Now, since we are discussing whether theta is less than half and more than half, one natural test we can think of is when more number of ones or in fact, all R1s may be that is theta greater than half, otherwise it is less than half that is one possible test and that is what let us define my region R that is the rejection region as something simply one all these ones. So, when all once I see I will reject it to be a null hypothesis, otherwise I accept it to be a null hypothesis. So, this is my rejection region has just one vector in that. Now, if I have to calculate the probability that under my theta, what is that X belongs to R? Now, X is I mean binomial, but I could think of like it is a Bernoulli with phi sample. So, this is nothing but we discussed last time this is nothing but simply probability that X1 is 1, X2 is 2, all the sorry X2 is 2, all the way to X5 is 1, all of them has to be 1 which is because of the independent nature, all of them with happened probability theta. So, this is like a theta to the power 5, ok. Now, let us compute type 1 error for this, ok. What is the definition of type 1 error? Definition of. So, what we basically got is this is the definition of our power function. What, how did we denote the power function? We denote it as beta of theta. So, this is like a beta of theta, ok. So, let us plot it. My theta is going to take value obviously between 0 to 1 and this is my beta of theta, ok. Now, how does theta to the power 5 look like? That is some polynomial curve, let us say it starts from 0 and goes till 1, let us say let us say this is like something looks like this. And let us say this is the half value and this is what my theta naught is this theta naught is actually half for me. So, when theta is less than half and I compute this probability that beta of theta, what this will give me? This will actually give me type 1 error, right. In this region because theta is less than half that is corresponding to the null hypothesis and I am rejecting the samples that is my type 1 error. So, in this region it is giving me type 1 error. Where are what is this is giving in this region? Now, theta here is greater than half that means, it is coming from alternator hypothesis, but this probability is still that of rejection, ok. So, what I am basically doing is I am theta is now in the compliment in the null hypothesis part sorry, alternator hypothesis, but I am actually still plotting this only, right not 1 minus. So, this is actually giving me the compliment of the error probability. So, this is like. So, in this portion this is type 1 error sorry, yeah in this portion it is type 1 error and in this portion it is 1 minus type 2 error, right. Now, we know that this function is increasing in theta, what is the maximum value of type 1 error here is? So, the type 1 error is happening here the maximum value of type 1 error happens when theta is equals to half and that is why we have written maximum type 1 error is half to the power 5 that is 0.0312, ok. Now, let us look into the type 2 error, right. So, what is the type 2 error now? What will be its. So, let us now let us try to actually compute its smallest value, ok. Now, 1 minus this is going to give you 1 minus type 2 error is going to give you or that will be represented by this region, ok. Now, maybe just if I look into the compliment of this maybe it will go something like this, I am just like trying to do the compliment of this, right. This is like this is basically 1 minus theta to the power 5, right. Beta 1 theta is anyway this is defined for every theta and that is theta to the power 5. And since beta 1 of theta is increasing in theta, if when theta becomes largest value 1 then it will take the smallest value that is going to be 0. That means, there would not be any type 2 error if theta is already 1, right. But now the smallest value is going to happen for this when theta is going to be half and when I plug half here that is basically this value, you will see that you are going to get this is actually we saw that last time this is kind of approximately 0.97, ok. So, you see that type 1 error is very small that you rejecting a sample which is coming from a hypothesis from a null hypothesis is very small. On the other hand type 2 error also very high, right. It may happen that your sample is coming from alternate hypothesis, but you may end up accepting it very good amount of time, but that is a bad case for us, right. So, one this is happening because we are looking at a very bad test, we are asking that when everybody is 1 that time only I am going to reject otherwise I am going to accept it to be null hypothesis. So, you can relax this test and say that instead of all to be 1 when the majority are 1 maybe I will reject otherwise I will still accept. So, in that case we are going to reject only when there are 3, 4 or 5 axis successes and you can compute the corresponding power function for that to be like this. And it so happens that you can also plot this function and this will something turn out to be like this. This is for beta 1 and this is for beta 2. So, notice that in this region which is giving me the type 1 error, beta 1 there test 1 is good because it has a low 1 here, but it was taking hit in the type 2 error. On the other hand if you now look into the beta 2, beta 2 has a higher type 1 error compared to sorry this type test 2 has a higher type 1 error compared to test 1, but what about this type 2 error? So, type 2 error is the complement of this, right. So, since this large compared to this that type 2 error is going to be lower. So, there is always a trade off. It is not that one test is going to give you a small type 1 error, it not necessary that it also give you small type 2 error. There may be other test which may give you smaller type 2 error, but it may end up having a type 1 error. So, we would always, but what you would I what you like ideally, we want both type 1 and type 2 error to be small that would be the best case, right. So, but that may not always happen simultaneously reducing them may not be possible. So, we have to keep that in mind whenever we are designing a test. So, we discussed this again I think last time we did the computation of this, right. I am not going to discuss this again when we have this samples coming from a Gaussian distribution with parameter theta and sigma square and where theta is unknown, but sigma square is known we can come up with our rejection region through this condition, ok. I hope all of you followed the derivation of the last time this is for a given c see something parameter that has been given to you. Now I can define now I know my rejection region I can define my power function for a given theta. So, the power function at point theta is simply probability that this ratio is going to be larger than c that is coming from everybody agree till this point basically we know that probability of theta is probability that my x belongs to the rejection region and this rejection region is captured by this that is why we follow. Now I can do a simple manipulation here, right. What I can do is on this left side I simply add theta and minus theta and I return one theta here and the remaining theta minus theta naught minus theta I move to the other side, ok. Why I have to do this? Now if you notice that so, by the way this probability under the parameter theta, right that is the definition say it as, ok. Now what is this quantity now? x bar now all these samples here are coming from PDF with parameter what? So, the samples that I am going to deal with here when I am computing this probability they are coming with the PDF parameter theta that is the meaning of this notation, right. Now so, what will be the expectation of x bar? It is going to be theta, right. What is x bar sample mean? And I am so, that basically have centralized and sigma by square root of n I am normalized it. So, what this random variable is going to be? So, we have seen this much before also, right. This is going to be a normal distribution and that is why I have represented it by z where z is a normal distribution or Gaussian with parameter 0 1 and that being larger than this. And I know how to compute this probability for a given c theta naught theta sigma and the square root n I know how to compute this probability. Any questions so far on this computations? Now I said in the last example both type 1 error type 2 error simultaneously you cannot play because we should try to reduce one other may increase. So, often we may be specified some value I want this much of type 1 error and this much of type 2 error, ok. How to guarantee that then, ok. Now recall that your power function depends on multiple factors one is the c that you are going to use in your test, right. What is the threshold you are going to use in your likelihood ratio test and also how many samples that you are going to use in performing this test, ok. And of course, what is the threshold you are using to define your defining your null hypothesis and the alternate hypothesis and theta is of course, your input parameter in this function. So, if I am going to change this c and n obviously, my power function value is going to change which is in turn is going to change your type 1 and type 2 error, right. So, somehow if somebody ask you ok I want this much of type 1 error and type 2 error then how is it possible for you to give him that kind of type 1 and type 2 error. So, what is in control what is in your control here to through what you can control or change your type 1 and type 2 error here, see ok. If you change c or type 1 and type 2 error will change maybe that is one thing you have in your control and n number of samples that is another thing which in your control by paying with it you can again control type 1 and type 2. Now, if somebody is asking you ok I want this much of type 1 and type 2 error maybe then you can see what is that c and n that can give you that much that kind of a type 1 and type 2 error, ok. Let us look into that. Suppose somebody ask you see I want type 1 error to be at most 0.1, ok and also type 2 error to be at most 0.2 when my theta is going to be greater than theta naught plus sigma. When this some condition you will see why this is coming then somebody is asking you already I want this much of type 1 error and this much of type 2 error. So, the only thing that you have in your control is c and n. Now, you need to decide what c I have to use, what n I have to use so that I can guarantee this, ok. Let us try to see how can I choose my c and n, ok. So, let us get started with this power function we have, this I hope from the previous slide it is all clear to you. Now, let us see this is a let us try to look into this a little more carefully as a function of theta. So, recall z is a standard normal distribution.  Everybody see agree? 1 are you sure? Ok. So, as theta goes to minus infinity this entire quantity becomes infinity minus infinity, right basically. And it does not matter what is the value of c because this guy dominates this c irrespective of what is this, this guy is going to be minus infinity and we know that probability z is greater than minus infinity is 1. On the other hand what value if I let theta go to minus infinity it is going to be 0 everybody agree? So, as I go from minus infinity to plus infinity am I going from 0 to 1 in a linear fashion or like in an increasing fashion? Yes. Yes. Ok. So, if I put this theta. So, as theta goes to infinity this is going to be 1 and as theta is minus infinity this is like something like this as a function of theta. Notice that this is not a CDF function I am plotting it as a function of theta now, ok and this is like 1. Now, based on this understanding can we now decide what should be the value of c and n. See first it is saying first one is type 1 error to be at most 0.1. So, the maximum value of the type 1 error should be 0.1. Now, can you tell me what is the maximum value of type 1 error here and notice that theta this is my theta and here it is below this it is type 1 and above this is 1 minus type 2 error. Now, what will be the maximum value of type 1? So, this is where my type 1 error is and this type 1 error is happening at equals to this, right. So, my maximum value of type 1 error is actually at beta equals to theta what is this value probability that z is greater than or equals to c and which you have been told you to be said to what value 0.1. Now, from this can you find out what is the value of c? How is that? So, you know that z has to be greater than or equals to c is 0.1 you know exactly at what point your standard normal is going to take value 0.1 like at what point if it exceeds it will take value of 0.1 you can find that. So, you find out now value of c. So, this will give you have so far figured out c. Is there something else you need to figure out? Yes. And also you need to figure out how to do that and now. So, for that let us use a second condition that your type 2 error has to be at most 0.2. So, I said type 2 error is like a complement of this it can be like something like just complement of this right when theta is going to be greater than equals to theta. Now, this quantity has to be at most 0.2 when theta is going to be larger than theta plus. Now, if I look into the type 2 error is type 2 error is going to be increasing or decreasing function in theta. So, type 2 error is now going to follow from 1 minus beta theta right and we know that if beta theta is increasing 1 minus beta of theta has to decrease and its maximum value happens when theta equals to theta naught. But we have been told that when theta is greater than theta naught plus sigma that time this value should be at most 0.2. So, you just plug in theta equals to theta naught plus sigma you will get. So, what you want is I want this quantity at theta to be at theta naught plus sigma to be 0.2 and now let us see what is beta of theta plus sigma if you plug in if you plug in here this is like a theta right this will knock off this theta I will get minus sigma that will cancel with this. So, I will get probability that z is greater than or equals to c minus square root n to be do I get this condition or maybe let me write this like a properly. Now, p minus z is greater than or equals to c minus square root n equals to 0.2 and c you have already decided from this. So, plug in that c and now what is remaining is only n is the quantity that is remaining and again by using your tail distributed properties of your CDF like CDF of your standard normal distribution you should be able to find out what is n ok. So, if somebody has to ask you to control they control your type 1 and type 2 error the thing that is in your control is what is the c value you can choose and how many samples that you want to guarantee that type 1 and type 2 errors ok. So, if you fix a number of sample maybe it is almost not possible or almost impossible to make both type 1 and type 2 errors to be small ok. That is why often in practice what we do is we say that let us my primary criteria is going to be on type 1 error let us guarantee that type 1 error is always going to be less than this much and after that see that what is the smallest type 2 error you can get ok. So, in a way if you want to look this into the from the optimization point of view what you want to do is you have been asked to give type 1 error to be let us say some quantity let us call let us call that to be alpha and now what you want to do is minimize your type 2 error. So, you want to find a test. So, this is across all tests. So, for every test is going to be associated with type 1 and type 2 error and you have been already told ok type 2 error cannot be that is my hard constraint type 1 error cannot be more than alpha if you satisfy that is good, but I will be also more happy if you make my type 2 error also small ok.