Question

A poll finds that 54% of the 600 people polled favor the incumbent. Shortly after the poll is taken, it is disclosed that the incumbent 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

Answer 1

Answer:

The value of z test statistics is 1.561.

Step-by-step explanation:

We are given that a poll finds that 54% of the 600 people polled favor the incumbent.

Shortly after the poll is taken, it is disclosed that the incumbent had an extramarital affair. A new poll finds that 50% of the 1030 polled now favor the incumbent.

Let $p_1$ = population proportion of people who favor the incumbent in the first poll

$p_2$ = population proportion of people who favor the incumbent in the second poll

So, Null Hypothesis, $H_0$ : $p_1\geq p_2$      {means that his support has increased or remained same after the second poll}

Alternate Hypothesis, $H_0$ : $p_1 < p_2$    {means that his support has decreased after the second poll}

The test statistics that would be used here is Two-sample z test for proportions;

                             T.S.  =  $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$  ~ N(0,1)

where, $\hat p_1$ = sample proportion of people who favor the incumbent in first poll = 54%

$\hat p_1$ = sample proportion of people who favor the incumbent in second poll = 50%

$n_1$ = sample of people in first poll = 600

$n_2$ = sample of people in second poll = 1030

So, the test statistics  =  $\frac{(0.54-0.50)-(0)}{\sqrt{\frac{0.54(1-0.54)}{600}+\frac{0.50(1-0.50)}{1030} } }$

                                       =  1.561

Hence, the value of z test statistics is 1.561.