For this problem. We are given the following claim machines suspense amounts with standard deviation greater than 0.15 oz and we have the following information off to the side. So the first for this hypothesis tests the state or no hypothesis. So each not. We're talking about standard deviation. So sigma And it's gonna be our 1.5 oz are alternative since the claim is stating greater than it'll be sigma, Somebody greater than 0.15. So once we have our go on alternative hypothesis, let's find our testes cystic. Since we're talking about sanity, aviation, we're gonna be using the chi square distribution and the chi square testes cystic can be found by and before end minus one times as squared divided by sigma squared. Yeah, So this is going to be 27 -1. Yeah. Time 0.17 Squared Divide by 0.15 Squared. And the chi square tests should be approximately equal to 33 points 396. So I was the testes cystic, you can do the p value. There's two ways to do the people, you can either do since the sample size 27 we have a degrees of freedom. 26 But in the end -1. Since this degrees of freedom is relatively small, we can find it within the table or we can find the inequality arranged within the table. And since this is a right to test and the high score table, I'm using finds area right to the tip. Other critical values what we wanna do. We don't want to go down the degrees of freedom. Do we get to 26? We want to find the range where 33.396 is between the two numbers. So I found that is between 17 point 292. And it's gonna be less than 35 point 563. So now if we go all the way up we'll find that probably are the area to the right of the curve. So the 17.292 equivalent to 0.935.563 equivalent to 0.1. And now we have our P value. So RP values between 0.9 or 0.1 and 0.9. A more accurate where you can get your P value though is using software is like our you use the Arco p chi square which does it take the input of your chi square testes, cystic degrees of freedom and then lower dot L. Equals true or false. So the lord dot tails telling us whether it's a left tail test or right tail test. Since the right tail test, you want that to be false. If you plug in this information we should get to this p value is about 0.1 509. Which again agrees within the table method table inequality. So if you have the p value can make a conclusion by comparing your p value. What's your alpha. But you can also find your critical values. To find your critical value of critical values. Your again going to your chi square table is gonna be Since we're doing air to the right we just want our alpha. And so we are degrees of freedom. Remember that our alpha is 0.05. Our degrees of Freedom 26. So if we go to our high score table we can find were those two intersect and are critical values. 38 .885. All right. So, you can make conclusion with the critical values and your testes cystic. If you have a chi square distribution looking something like that, you're critical value. The states here Just 38.885. Okay, so you're critical value. We will reject any or don't have process. If it falls within this blue region, this is also called our rejection region. And if it falls anywhere within the non stated region, we will accept it. Which is also called our acceptance region. We see our test statistic as 33.396. So if you try to play set somewhere here that maybe belong around over there. Yeah. So that's archive square test. Yeah. And it falls within our acceptance region. So in this case for comparing test statistics and critical values we fail to reject If you want to compare with the P value and alpha. So a p value is greater than alpha. We failed to reject. H. Not. Yeah. and if P value is less than alpha, we reject H. Not again, we can look really quickly. We have AP value of 0.1509. And after a value of 0.05, our p value is greater than our alpha, so we failed to reject the null hypothesis. So in both cases we came to the same conclusion, which was we fail to reject H not.