So for this problem we're told the significance of 0.01. The claim is that we pennies are manufactured so that the waves have a standard deviation equal 0.0-30 graphs. And for this problem we want to identify them. No alternative hypothesis testes is six p values, critical values and the make a claim based on what were the data we did based on our process. So, first there's an empire, the no hypothesis. Alright, highlight that this is a protesting for sanity, aviation and that this equals 0.0 230 g from the claim. Yeah. The alternative, we're still testing Sander deviation but there is no greater than or less than So we don't really care as long as it does not equal 0.023 g. So this is a two tailed test. So secondly, let's now find our testes cystic. Yeah. For the test statistics, since we're testing the standard deviation, this is gonna be a chi square distribution. And we can find it to be M -1 squared divided by sigma squared where n is the length of the data. And as squared you can find using this form from the data And if you plug this in, I got a testis cystic of three points 81 for all right. So, once you have that, you can find your p value, you can find the p value is one of two ways either through the table. Um but if you do it through the table method, you won't get an exact value of finding a range that your p value falls under. Or you can use technology like our our stack crunch, which will give you a more accurate p value. So the main function in our final p values where chi square distribution with bp Yeah. Hi, square. And then we're going to have our testes cystic Degrees of freedom and -1 and we're gonna have this lower dot tail equals something At one point on this is a two tailed test. So this p value around to multiply this p value by two and remember this P value is a probability. So if we say the p value is equal to false and we get greater than one then we might we might not be doing the right tail. So let's try P value is equal to true. And we get a p value of zero point two five three and we like this because the p value still less than one. If you were to try this with the lower tell equals of false, you should get a p value greater the one which is not which is no longer a probability. So remember we can make in conclusions. If the p value, it's greater than alpha, we will accept the null hypothesis. Yeah. And if the p value less than alpha, we will reject no of assists. And here we can see that 0.253. Well that's greater than our alpha which is 0.01. So we should accept on our policies process for the sake of completion. Find the critical values and compare it with our testes cystic. Yeah. So you can use the table again. Find the degrees of freedom and alpha. But if you you the degrees of freedom or we're going to be chi squared with one minus off over to degrees of freedom and chi squared Alpha over 2° of freedom. Yeah. And from the table you should get the numbers. You can also use technology like our the functions are gonna be the same will be q chi square and for the most part inputs are the same. You're gonna putting off over to Your N -1. The only thing that's going to change is this lower dot tail. So we're gonna have one that's lower dot l equals true. And this gives him one 34. Yeah. Another one. The whole q chi square alpha over to and -1. Lower dato equals two false. And this gave me 21 point 955. So how do you make conclusions based on the critical values and the testes cystic. So if we have a high score distribution We have these points. The 1.34 And the 21.96. These are giving us two different areas and these are gonna be our alphas over to And both of these are gonna be our rejection region. So if our tested falls within those areas, we reject ever if it falls within the middle, that is our acceptance region. So we won't we will accept our normal processes. So we go back to see what our test statistic was. This is 3.814. So that falls probably somewhere around here, or this was our testes statistic. So again, our testes, it falls within our acceptance region. So we will accept the null hypothesis was which was the same conclusion. We came with the P values in alpha. So This is not statistically significant alpha level of 0.01. So we will have to accept that the standard deviation is equal to 0.023.