Answer:
The test statistic is Z = 1.157
Step-by-step explanation:
Given that:
The sample size n = 1200
The sample proportion of those that will vote for the Republican candidate is represented by [tex]\hat p = \dfrac{x}{n}[/tex]
[tex]\hat p = \dfrac{620}{1200}[/tex]
[tex]\hat p =0.5167[/tex]
The null and the alternative hypothesis can be computed as:
[tex]H_o: P=0.50 \\ \\ H_a :P>0.50[/tex]
The formula for the one-sample Z-test for the population proportion can be expressed as:
[tex]Z = \dfrac{\hat p - P_o}{\sqrt{\dfrac{P_o(1-P_o)}{n}}}[/tex]
[tex]Z = \dfrac{0.5167 - 0.5}{\sqrt{\dfrac{0.5(1-0.5)}{1200}}}[/tex]
[tex]Z = \dfrac{0.0167}{\sqrt{\dfrac{0.5(0.5)}{1200}}}[/tex]
[tex]Z = \dfrac{0.0167}{\sqrt{\dfrac{0.25}{1200}}}[/tex]
[tex]Z = \dfrac{0.0167}{\sqrt{2.08333333\times10^{-4}}}[/tex]
Z = 1.157
Testing the hypothesis, from the information given, it is found that the test statistic is z = 1.157.
The null hypothesis is:
[tex]H_0: p = 0.5[/tex]
The alternative hypothesis is:
[tex]H_1: p > 0.5[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
For this problem, the parameters are: [tex]p = 0.5, n = 1200, \overline{p} = \frac{620}{1200} = 0.5167[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.5167 - 0.5}{\sqrt{\frac{0.5(0.5)}{1200}}}[/tex]
[tex]z = 1.157[/tex]
The test statistic is z = 1.157.
A similar problem is given at https://brainly.com/question/24166849
