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:

Price Decreases

A reduction in the cost at which goods and services are sold in the market.

Net Seller

An individual or entity that sells more of a security, commodity, or other assets than they buy in a given period.

Quasilinear Preferences

Preferences where the utility function is linear in one argument, often money, which allows for easy analysis of changes in welfare from different quantities of goods.

Consumer's Surplus

The variance between what consumers are prepared and capable of spending for a product or service and the actual sum they end up paying.