Question

One of the more popular statistics reported in the media is the​ president's job approval rating. The approval rating is reported as the proportion of the population who approve of the job that the sitting president is doing and is typically based on a random sample of registered voters where the sample size is the same week to week. Complete parts​ (a) and​ (b) below. ​a) This proportion tends to fluctuate from week to week. Name some reasons for the fluctuation in the statistic. Select all valid reasons below. A. The proportion could be changing because the sampling size of the poll is changing. B. The proportion could be changing due to a large change in the composition of the population. C. The proportion could be changing due to sampling​ error; different people are in the sample. Your answer is correct.D. The proportion could be changing because​ people's attitudes are changing. Your answer is correct.

​b) A poll showed the approval rating to be 0.51 ​(51​%). A second poll based on 2000 randomly selected voters showed that 968 approved of the job the president was doing. Do the results of the second poll indicate that the proportion of voters who approve of the job the president is doing is significantly lower than the original​ level? Explain. Assume the alphaequals0.05 level of significance. Null and alternative hypothesis. H0p=.51, H0p <.51

I only need help with these questions(not sure how to set it up) :

Determine p-value for this hypothesis test

State the conclusion for this hypothesis test.

Find the test statistic for this hypothesis test. zequals nothing ​(Round to two decimal places as​ needed.)

Answer 1

p=51​% =0.51, n= 2000, x= 968, = 0.05

Ho : p = 0.51

Ha: p < 0.51

Calculate test statistics

z = −2.326

z = -2.33

Test Statistics Z = -2.33

P-Value = P(z < -2.33)

find P(z < -2.33) using normal z table we get

P(z < -2.33) = 0.0100

P-Value =  0.0100

since (P-Value = 0.0100) < (= 0.05)

Reject the Null Hypothesis

Therefore there is enough evidence to claim that the proportion of voters who approve of the job the president is doing is significantly lower than the original​ level at  = 0.05.