In this question. We want to compare the average earnings of college graduates whether they're men or women, and is there a difference? And if there is a difference in income, what is that different in income between men and women? When he was hypothesis testing specifically the Z test presented at page 4 91 of the book because started Step one gather over data so we know that it started with the simple sites for one. So we know we simple the 100 men. So 100 men and 100 women and those simple we The average earning for men was 90 1002 $100. For women, it was lower. It was 57,000 $800. The standard deviation for all mental not just for a sample for the population of men is $15,000. For women, it's 12,000 $800. We're gonna right now, our hypotheses. So the no hypothesis is based on the question should be that the difference in price the difference in the present earnings or income is exactly $30,000. What is claimed in the question is that this difference is not $30,000 So we will have a two tailed tests as soon as I finish writing this. So the difference in income or earnings and not exactly sure the difference. I'm not economy major. So, uh, the difference is not $30,000 So we have a two tailed tests. Therefore, rejection area is this thing this area in red. So to tell our normal distribution now that we have our hypotheses, you have Oliver data our data that's going to step two. So step to want to find our critical value. We know that Alfa is 0.1 Therefore, Alfa over to is 0.0 Ah, another 05 So are critical values are plus minus yes. Close or minus two 0.575 minus 2.575 on the left of our graph and 2.575 on the right hand side of our graph ever critical value. Now we need a zeke to compare those critical values to. So Step three, figure out Z Z is the difference in earnings for our samples. Ah, I wrote it s because I was thinking simple, but it's w four women. Mine is the difference in earning for all men and all women divided by the variants in earnings for men divided by the number of men. Simple. Plus that the variants in earnings for women divided by the number of women. Simple. All of that inside a square root. Remember, H zero tells us that this quantity is difference for you men and women Home. Oh, minute on women is $30,000. So what we have for Z world be 90,000 200 minus 57,000 800 minus 30 1000 over 15,000 squared, divided by 100 plus 12,800 squared, Also divided by 100 Everything inside a square root. I will let you plug all those values in your calculator or your computer, and you will get a value of 1.21. Let's go compare debt Z value to the critical value found that step to so Z is 1.21 1 point. Anyone that say it's right here in any case is smaller than 2.575 So we're not in the rejection area, so we do not reject age zero. We accept with those samples we accept h zero. So since one since 1.21 is smaller, then 2.575 and we do not reject 80 which means the difference in mean income. Four man and women is 30 $1000 sell quick recap. We gathered all of her data for problem. We rolled down her hypotheses and figured out critical values to define a rejection area. Computed rz two see if it was in their rejection area and we decided, since it wasn't in the rejection area, we did not reject age zero and we concluded that the difference in mean and come for men and women is $30,000.