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

Step-by-step explanation:

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

As per given , we have

$H_0: p=0.54\\\ H_a: p$

Sample size : n= 1030

sample proportion :  $\hat{p}=0.50$

Test statistic for proportion : $z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

$z=\dfrac{0.50-0.54}{\sqrt{\dfrac{0.54(1-0.54)}{1030}}}\\\\= \dfrac{-0.04}{\sqrt{\dfrac{0.2484}{1030}}}\\\\=\dfrac{-0.04}{0.015529488}\approx-2.57$

Hence, the  test statistic is z = -2.57 .

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