To Test the Null Hypothesis That the Difference Between Two

Essay

To test the null hypothesis that the difference between two population proportions is equal to a nonzero
constant c, use the test statistic: $$z = \frac { \left( \hat { p } _ { 1 } - \hat { p } _ { 2 } \right) - c } { \sqrt { \hat { p } _ { 1 } \left( 1 - p _ { 1 } \right) / n + p _ { 2 } \left( 1 - p _ { 2 } \right) / n _ { 2 } } }$$ As long as $n _ { 1 } \text { and } n _ { 2 }$ are both large, the sampling distribution of the test statistic 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 significance
level of 0.10. Men: $n _ { 1 } = 250 , x _ { 1 } = 146$
Women: $n _ { 2 } = 202 , x _ { 2 } = 103$