Question

poll finds that 54% of the 600 people polled favor the incumbent. Shortly after the poll is taken, it is disclosed that he had an extramarital affair. A new poll finds that 50% of the 1030 polled now favor the incumbent. We want to know if his support has decreased. The test statistic is A. z = -2.57. B. z = 1.56. C. z = -1.55.

Answer 1

Answer: A. z = -2.57

Explanation:

Let p be the population proportion of people polled favor the incumbent.

As per given , we have

`H_0: p=0.54\\\ H_a: p<0.54`

Sample size : n= 1030

sample proportion :
`\hat{p}=0.50`

Test statistic for proportion :
`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}`

`z=\frac{0.50-0.54}{\sqrt{(0.54(1-0.54))/(1030)}}\\\\= \frac{-0.04}{\sqrt{(0.2484)/(1030)}}\\\\=(-0.04)/(0.015529488)\approx-2.57`

Hence, the test statistic is z = -2.57 .

Thus , the correct answer is A. z = -2.57 .