"The Annual Report on the Economic Status of the Profession" done by the American Association of University Professors, the mean salary of a full professor was reported to be $\$ 83,282 .$ The table below lists the average salary (in dollars) for a random sample of institutions in Colorado. Using the computer output that follows, test the claim that the median salary of full professors in Colorado is lower than the mean for the whole country by writing the hypotheses and verifying the number below and the number above the median. Complete the test by using the $p$ -value given and $\alpha=0.05 .$ Verify the given $p$ -value using Table 12 in Appendix $B$.
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Okay, let's look at question 14 together here. So, um, our no hypothesis ISS The median is equal to 83,000 and two under 82. And the alternative hypothesis is that the media and is smaller than this amount of money. Um, because here, the sign is smaller than so, which means we're looking at the one talk situation. All right, um, by looking at the table list at the low, we know that the sample size is 20. And, uh, and off Linus is 16 and off, plus is four. So our X star that is going to be, um, is going to be four, cause for a smaller than 16. All right, um, So what we're going to do right now is that we're going to look at table 12 and find the corresponding line for Enos. He go to 20 so Oh, just try here. Can the above, Because their own point. There are one narrow mind. No, by their white one 0.2 by and we have three high by six and know that here are Crippen. Our X star is four. So four is in between three and five. So which means our P value should be tweeting between their open, their one divided by two here and smaller than their opine. There are five D bye bye to the result women to divide by two year. Because instead of looking at to tell situation, we're actually looking at one type situation. So we need Teoh, um, divided by two and which is going to be, um, people greater than their A 0.5 and smaller than the aeroplane. There are 25 And from the question we know that the ec Tropea Vallo calculated by the computer is Geico to their A pine. There are there, 05 night and is in between the pounds. We just find out. So, um