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

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: $\mathrm { n } _ { 2 } = 202 , \mathrm { x } _ { 2 } = 103$