 Hi, this is Don again, and I keep seeing people missing problems Either normal distribution problems or t-distribution problems or paired sample problems because they don't set up the Null in the alternative properly and to do that you've got to read the question very carefully in this question It gives us that the claim is that mu1 Is less than mu2 if the claim has an Inequality for an operator that is a less than greater than or not equal then the claim has to be the alternative apothesis the null would be the Opposite the complement of the alternative in this case that would be mean one mu1 might is Greater than or equal to mu2 so once you know the Null and the alternative you have what you need to do to solve the problem and We're going to do this with stat crunch open that up so we can see everything and We're given data on two samples. We're given the Sample means the sample standard deviation and the count in each of the two samples. So we'll go to stat Z stats to sample was summary and bring up this dialog box the first mean is 112 20 Standard deviation 75 in 35 X bar 2 is 1 1 9 0 Standard deviation 1 1 0 and the N is also 1 1 0 now Here's the the critical part is setting up the hypothesis the default is that Mu1 minus mu2 is 0 and now we know that's not the case in ours our alternative is not that the difference is 0 but the difference is going to be less than 0 if Mu2 is greater than mu1 then that difference will be a negative and Thus less than zero. So if we get that alternative set up Then the null even though it just shows the equality remember in stat crunch and most stats programs we solve these two sample tests With a null of equality if it is significant for the null of equality Then it is also significant for everything greater than equal as well So let's click on compute And we get our answer there. We see that our sample mean Mu1 minus mu2 is 30 and that's the answer to the first question the test statistic The second question is the standardized test statistic and there we get it from Statcrunch 1.823 or 1.82 and It asks is the standardized test statistic in the rejection region? Well, we don't even have to look at the graph because we're given a p-value Here and because the p-value is far far greater than our alpha I think our alpha in this one Yeah, there it is point zero one. So the p-value point 966 is much much greater. Therefore we failed to reject the null hypothesis and just for fun Let's just look at the critical area. They give us this little sketch You can blow it up to see it better We can see that the critical area the rejection the critical value rather is minus two point 33 and the rejection region is Everything to the left of that are less than minus two point three three our Z stat is 1.82 that's over here on this side. So it's definitely not in the rejection region. Hope that helps folks there was one thing I forgot to mention at the tail end of that last video and That was this final question. Should we fail To reject our reject a null hypothesis the first part we answered We failed to reject because we had a very large p-value and also because the test statistics Did not fall in the rejection zone the second part of the final question is Something that gets people a problem as well and it relates back to setting up the claim properly At the 1% Significance level is there enough or is there not enough evidence to support the claim? Well, we failed to reject the null the null Was not the claim the alternative was the claim Since we failed to reject the null that means there is not enough evidence to support the claim Which was the alternative hope that helps