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 = <u><em>population proportion of people who favor the incumbent in the first poll</em></u>
= <u><em>population proportion of people who favor the incumbent in the second poll</em></u>
<u><em /></u>
So, Null Hypothesis, :
{means that his support has increased or remained same after the second poll}
Alternate Hypothesis, :
{means that his support has decreased after the second poll}
The test statistics that would be used here is <u>Two-sample z test for</u> <u>proportions</u>;
T.S. = ~ N(0,1)
where, = sample proportion of people who favor the incumbent in first poll = 54%
= sample proportion of people who favor the incumbent in second poll = 50%
= sample of people in first poll = 600
= sample of people in second poll = 1030
<u><em /></u>
So, <u><em>the test statistics</em></u> =
= 1.561
Hence, the value of z test statistics is 1.561.