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> = ![\frac{(0.54-0.50)-(0)}{\sqrt{\frac{0.54(1-0.54)}{600}+\frac{0.50(1-0.50)}{1030} } }](https://tex.z-dn.net/?f=%5Cfrac%7B%280.54-0.50%29-%280%29%7D%7B%5Csqrt%7B%5Cfrac%7B0.54%281-0.54%29%7D%7B600%7D%2B%5Cfrac%7B0.50%281-0.50%29%7D%7B1030%7D%20%20%7D%20%7D)
= 1.561
Hence, the value of z test statistics is 1.561.