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

question 6

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 $$z = \frac { \left. \hat { \left( \mathrm { p } _ { 1 } \right. } - \hat { \mathrm { p } _ { 2 } } \right) - \mathrm { c } } { \sqrt { \hat { \mathrm { p } } _ { 1 } \left( 1 - \hat { \mathrm { p } _ { 1 } } \right) / \mathrm { n } _ { 1 } + \hat { \mathrm { p } } _ { 2 } \left( 1 - \hat { \mathrm { p } } _ { 2 } \right) / \mathrm { n } _ { 2 } } }$$
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 10 percentage points more than the percentage of female voters who plan to vote Republican. Use the traditional method of hypothesis testing and use a significance level of $0.05$ .
Men: $\mathrm { n } _ { 1 } = 250 , \mathrm { x } _ { 1 } = 146$
Women: $\mathrm { n } _ { 2 } = 202 , \mathrm { x } _ { 2 } = 103$

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Definitions:

Hourly Wage

The amount of money paid to an employee for each hour worked, often set by legal minimum wage laws or by agreement between employer and employee.

Fringe Benefits

Fringe Benefits are additional benefits supplementing an employee's salary, such as health insurance, paid vacations, and retirement plans.

Winner-Take-All Markets

Markets in which the top performers or companies receive a disproportionately large share of the rewards, and the remaining competitors are left with very little.

Hourly Wage

The amount of money paid for each hour of work.