 Hi Eileen. This is Don. I think this is the problem that you're talking about when you said problem 11 in section 7.2 and it has to do with Using the normal distribution to solve a hypothesis test and really using stat crunch It's pretty quick and easy and I'll walk you through the steps on how to do that Because we have this little icon here We can click on that and then our options are to open in stat crunch or an excel right now I'm going to open in stat crunch That'll take a second for it to come up and We have our data here Whoops, where'd it go? There it is and the first column label variable 1. We've got 30 data points and We want to solve this Hypothesis test we go to stat Z stats one sample with data and we get this dialog box Now the data that we want to operate on Variable one so we can just double click that to load it into the right side We don't have to enter the standard deviation that we don't have to worry about these next three items because we have the raw data and One thing to remember You know that we can use the Z test for this Because we have an N of 30 or more and if you're 30 or more then you're pretty sure that the Sampling distribution is also normal We need to set up the hypothesis test the value that we're Looking for let me pull this down for a minute and look at it You had made a mistake on setting up the no and the alternative The wording was that the manager thinks that the salaries The politician. I'm sorry thinks the salary for managers in his state is more than the national mean 5,000 more than tells you that it's The hypothesis has a greater than symbol in it and remember our rule of thumb the no hypothesis always has some form of Equality and that can be less than or equal equal or greater than or equal Since the other alternative has a greater than symbol that has to be the alternative and Looking at the six options here The one you checked is just the reverse you put greater than or equal Remember the politician said it to greater than If he had said at least 83,000 then you would have been right It would have been greater than or equal Greater than or equal always is in the null and the alternative would be the less than but in this case He said more than or greater than that means a greater than symbol in the equation So that's our hypothesis. So now let's go back into stat crunch our null is 83,000 and remember I said that in stat crunch and mini tab and Excel stat and other Statistics programs when you're running these hypothesis tests You just run the test for the equality in this case that the mean of the population is Is equal to 83,000 if we run this test and it is significant For the equality that means it will also be significant for Everything greater than 83,000 the greater than part of the test what is critical here is setting up the alternative properly remember we have a greater than symbol in our Alternative hypothesis, so we've got to get that in that makes it a one-tail Upper-tail test everything to the right in the normal distribution curve So we just click on compute and we get our answers and I'm going to drag this down So we can see better here It calculates the Z stat for us 1.734 they rounded it to 1.73 and See you entered 0 to 7 so you got that wrong But the stat crunch gives us that value and even if you had rounded up to 1.74 I would have found it and given you credit for that. The second part is what is the p-value and the p-value Stat crunch gives us point 0 4 1 4 and again that would technically round to point 0 4 1 Just barely and stat crunch says point 0 4 2 a little bit different But I would have given you credit obviously point for point 0 4 1 the last part of the Problem decide whether to reject or fail to reject the null hypothesis We know that the p-value point 0 4 is less than the alpha point 0 8 Therefore we reject the null and since we're rejecting the null We have to decide is there sufficient evidence to support the claim or Is there not sufficient evidence to support the claim? Well in this case We reject the null and the claim was the alternative Since we're rejecting the null that means we're supporting the claim and Therefore there is sufficient evidence to support the claim. I hope this helps Eileen there was one thing that I forgot to show you about Stat crunch and the hypothesis test Once you get these values there if you go back you can click on options and edit and Down here at the bottom is what I forgot to mention you can have plots Of the data and of the situation What is helpful is this p-value plot since that's what we're Questioning and as I said before it's always helpful to draw a sketch of your relationship between The mean and the value in question so if we select that p-value plot click on compute We still have our our data, but down at the bottom you've got this little Link to click on and it will show you the p-value Plot and as I said because our alternative was a greater than that Points to the right and that tells us this is an upper tail test a right tail test our rejection area would be everything over here in this red and Although we don't have the critical value of p plotted on here we know that with our p-value of point oh for our test statistics of 1.7346 falls in this critical red area, so I hope that helps I'm going to show you one final thing that you can do with Stat crunch to help with these Let's calculate what that critical value of C is Z is the critical. I'm going to go to stat calculators normal and we bring up this Rough sketch We want the standard because we just want to know the upper tail tests are We want to click on upper tail to begin with point to the right And we want to put in our alpha value point zero eight And we use the entire alpha value because this is a one tail test if this were a two tail test You would put in half of alpha, but we click on compute and We get our critical value of Z of one point four oh five and Can't really let me see if I can stretch this here so we can see things see both of them there we go You can see that our Test statistic is one point seven three our Critical value is one point four one, which is right in here. So our Test statistic falls within this critical area that we always want to see so use those tools instead crunch to draw these These graphs to help you make sure that you're solving for the problem that you intend to solve for