Solve the Problem As Long As $\mathrm { n } _ { 1 }$

question 32

Essay

Solve the problem.
-To test the null hypothesis that the difference between two population proportions is equal to a nonzero constant c, use the test statistic $\mathrm{z}=\frac{\left(\hat{\mathrm{p}}_{1}-\hat{\mathrm{p}}_{2}\right)-\mathrm{c}}{\sqrt{\hat{p}_{1}\left(1-\hat{p_{1}}\right) / \mathrm{n}_{1}+\hat{p_{2}\left(1-\hat{p_{2}}\right) / \mathrm{n}_{2}}}}$ As long as $\mathrm { n } _ { 1 }$ and $\mathrm { n } _ { 2 }$ are both large, the sampling distribution of the test statistic $\mathrm { z }$ will be approximately the standard normal distribution. Given the sample data below, test the claim that the proportion of male voters who plan to vote Republican at the next presidential election is 15 percentage points more than the percentage of female voters who plan to vote Republican. Use the P-value method of hypothesis testing and use a significa level of $0.10$ .
Men: $\mathrm { n } _ { 1 } = 250 , \mathrm { x } _ { 1 } = 146$
Women: $\mathrm { n } _ { 2 } = 202 , \mathrm { x } _ { 2 } = 103$

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Definitions:

Mammary Glands

Specialized organs in female mammals that produce milk for the nourishment of newborn offspring.

Ceruminous Glands

Specialized glands located in the ear canal that produce earwax, which helps protect the ear from foreign particles and microorganisms.

Sebaceous Glands

Glands located beneath the skin surface, secreting sebum that lubricates hair and skin to prevent drying out.

Analysis of Variance

A statistical method used to compare three or more samples means by analyzing their variances.