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:

Price Increase

A rise in the cost of goods or services over a period of time.

Demand Curves

Demand curves graphically demonstrate how the quantity demanded of a commodity varies with its price, highlighting the inverse relationship between prices and demand quantities.

Substitute Good

A product or service that satisfies the need of a consumer that another product or service fulfills.

Important Resource

A crucial element or input required for the production process or societal functioning.