To Test the Null Hypothesis That the Difference Between Two

question 11

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

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Definitions:

Appliance Stores

Retail outlets specializing in the sale of electrical or mechanical devices used in homes.

Microwaves

Electromagnetic waves with frequencies ranging from 300 MHz to 300 GHz, widely used in telecommunications, radar, and kitchen appliances for heating food.

Non-accidental Deaths

Refers to deaths resulting from causes other than accidents, such as diseases or intentional harm.

P-value

The chance of getting test outcomes that are as significant or more so than what was actually seen, assuming the null hypothesis is true.