To Test the Null Hypothesis That the Difference Between Two

question 51

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

---

Definitions:

Direct Labor Rate

The cost of labor per hour for workers directly involved in the manufacturing process.

Cash Budget

A financial plan that estimates cash inflows and outflows over a specific period, helping manage liquidity and ensuring availability of cash.

Cash Receipts

The collection of money (cash, checks, wire transfers) by a business or individual, often recorded in the accounting records.

Finished Goods Inventory

The total value of all completed products that have not yet been sold by a company.