To Test the Null Hypothesis That the Difference Between Two

question 15

Essay

To test the null hypothesis that the difference between two population proportions is
equal to a nonzero constant c, use the test statistic $$z = \frac { \left( \hat { p } _ { 1 } - \hat { p } _ { 2 } \right) - c } { \sqrt { \hat { p } _ { 1 } \left( 1 - \hat { p } _ { 1 } \right) / n _ { 1 } + \hat { p } _ { 2 } \left( 1 - \hat { p } _ { 2 } \right) / n _ { 2 } } }$$
As long as $n _ { 1 }$ 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: $n _ { 2 } = 202 , x _ { 2 } = 103$

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Definitions:

Ordinary Annuity

A financial product where payments of a fixed amount are received at the end of equal intervals.

Nominal GNP

Gross National Product measured in current prices, without adjusting for inflation.

Fair Market Value

Fair Market Value is the price at which an asset would trade in a competitive auction setting, reflecting the amount a willing buyer would pay to a willing seller.

Constant Growth

A situation or model where values (such as dividends or revenues) increase at a steady, unvarying rate over time.