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hi professor, in section 8.6 problem 45. Why is x=255, and why do i not find ^p as x/n? I this problem is about finding the confidence interval for a population proportion?
thank you

Posted to STATS 1 on Tuesday, December 10, 2013   Replies: 1

Professor Mcguckian
12/10/2013
9:55 PM EST
Hi Natassia,

A senatorial candidate claims that most of the people in the country feel they are worse off today
than they were two years ago. A poll of 500 people in the country reveals that 255 feel they are
worse off today than two years ago. At the 10% significance level, test the senatorial candidates
claim.

Claim: p > 0.50 (most = more than half)

The claim talks about the percent of people feeling worse off today. This makes your x = the number of people who feel they are worse off today. Your X is the number of subject having the trait you are interested in. In this problem, that trait is feeling you are worse off. To get p-hat, we need to perform the calculation x/n, so that gives us: p-hat = 255/500 = 0.51

From that, we can find our test stat: (p-hat - p0)/Root(p0*qo/n) = (0.51 - 0.50)/Root(0.5*0.5/500) = 0.447213... = 0.45

This is not in the rejection region, so we do not reject the null. This means we do not support the claim.

Professor McGuckian