Answer to Question #293587 in Statistics and Probability for isaac

Question

a presidential candidate asks a polling to conduct a nationwide survey to determine the percentage of potential voters who would vote for him over his rival presidential candidate. out of 2 500 respondents in the sample, 945 said they would vote for. What course of action the presidential candidate must do based on the survey results

Answer 1

Question is incomplete, assume the question as follows:

A presidential candidate asks a polling organization to conduct a nationwide survey to determine the percentage of potential voters who would vote for him over his rival presidential candidate. Out of 2500 respondents in the sample, 945 said they would vote for him. If 40% of the potential voters vote for his rival, is this significantly different from the percentage of potential voters of the candidate who requested the survey? Use 5% level of significance.

Solution:

$p=\dfrac{945}{2500}=0.378, \hat{p}=0.4, n=2500$

$\alpha=0.05, Z_{\alpha}=Z_{0.05}=1.64$

Let $H_o:$ Claim is true that There is significantly different from the percentage of potential voters of the candidate who requested the survey.

and $H_a:$ Claim is not true.

Test-statistics-

$z=\dfrac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}=\dfrac{0.4-0.378}{\sqrt{\frac{(0.37(1-0.37)}{2500}}}=\dfrac{0.022}{0.00965}=2.28$

Conclusion: As calculated value of $Z$ is greater than the $Z_{0.05},$ so Null hypothesis is rejected. There is not enough evidence to support the claim that There is significantly different from the percentage of potential voters of the candidate who requested the survey.