 Hi Eileen, on this question you have about problems 7 in section 7.3 and you said when the question does not provide the standard deviation, how do I find it in stat crunch? Okay, let's look at the problem and I think this is the one and it is a question in which they want you to use a distribution to determine whether or not the sample supports a claim that the mean salary is $22,350 and they tell us to assume the population is normally distributed, there are two things that we need to first think about, one we only have 10 values in our sample, so that's a lot less than 30 so that would tell me that I probably want to use the t distribution for this particular question. And first thing I wanted to do is let's just look at the first part of the question, what are the null and the alternative? Once the claim is that the mean is $22,000, in other words the mean salary equals $22,350 that means it has to be the null, the null always has the equality, the alternative always has the inequality. So if the mean is $22,000 that means the null is mu is equal to $22,350 and if you look down here and you pick the right one, mu is equal to $22,350 that is the claim and the alternative has to be the complement which would be not equal to $22,350. Because we've got a not equal in the alternative that tells us we have a two tail test, a two tail test and I think that's the reason that you missed this problem there. You've got a value of 2.821 to minus 2.821. So let's check, I want to bring up stat crunch and we can do that here because we've got data and we've got the little icon. I'm going to open that in stat crunch and bring that up and the first thing I want to do is try to find this critical value of t. So we go into stat, t stats, I'm sorry, calculators, t calculator and we get this calculator. We want to use the standard because we're not doing it between and we're trying to find the critical value of t. The degrees of freedom is equal to n minus one. You've got ten values in the sample so that's n so our degrees freedom is nine. The alpha is 0.01 because we have a two tail test that means each tail has half of 0.01 or 0.005 and we'll click on compute and we can see that the left tail, the lower tail that has 0.005 probability or the area into the curve of 0.005 is a t of minus 3.2498 or 2. I'm sorry 3.250 rounding it off and that is the answer they had minus and negative and of course you can check the other side by putting the 0.005 in again and there again is your positive t critical of 3.250 so that's how they got that. Let me see if I if I put in 0.01 what do I get? 2.821 and I think that's what you got. So what you forgot to do was since you've got a two tail test you got to divide alpha by 2 to get the critical value. Okay let's solve the next part of this and we're going to go to stat t stats one sample with data and we bring up this dialog box and our data is in the column label variable one so we select that just double click on it and then down here we can leave the way or in group by alone we've got to set up our hypothesis test mu is 22.350 we make sure that alpha is the complement which is the not equal and I'm going to click on p value I'm sorry p value plot just to give us a little more information here and click on compute and we let me bring this up here so we can see a little bit better make it a little bit bigger bring that chart over there and spread this out here okay the results of the one sample hypothesis t hypothesis test for mu equal to 22.350 and the alternative mu not equal we get there's our degrees of freedom who said nine and we get a t stat of minus point six three one three a rounding to minus point six three one and I'm pretty sure yeah minus point six three is what they came up with see what did you come up with 190 I have no idea how you did that I think but anyway we've got our critical value our sorry our value of our t statistic of minus point six three we've got a p value here of point five four three five which tells us that the test is not significant and therefore we would not reject or we failed to reject the null hypothesis so let's just check something here I got it to give us this p plot and this shows the values from the t statistics minus six point three and that shows the positive side but this is the area under the curve to the left of our test statistic and you can see it's a lot larger than the critical area over here in this test you can just see the critical area there again believes it begins at minus 3.25 our t value here is minus point six three so that's definitely not in the rejection zone so we fail to reject both things tell us to fail to reject the the null we bring this down here and do the last part um what do we decide to do we fail to reject the null because the test statistic is not in the rejection region and also stat crunch gave us a p value which was greater than alpha much much greater which also says do not reject we fail to reject so the last part is interpret the decision and you got it right and the claim was the null we do not reject the null we fail to reject the null therefore there's insufficient evidence to reject the claim so that makes sense so I hope this helps Eileen I forgot to answer your basic question how do you solve this without the standard deviation being given and again they don't give us a standard deviation but they give you the data and when you use stat crunch with the raw data to solve the t hypothesis test stat crunch calculates the standard deviation from this data and it doesn't show it to you I don't think let me go back no it doesn't give you the standard deviation gives you the standard error that you can back calculate but trust me stat crunch was calculated did calculate the standard deviation and used it in this t hypothesis test and if if you're curious about it you can calculate that standard deviation yourself let's just go to to stat again summary stats column variable one and I'm just going to select standard deviation this time compute and there you have the standard deviation if you're trying to solve this thing longhand