Solve the Problem As Long As $\mathrm { n } _ { 1 } \text { and } \mathrm { n } _ { 2 }$

question 137

Essay

Solve the problem.
-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 $\mathrm { n } _ { 1 } \text { and } \mathrm { n } _ { 2 }$ 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 10 percentage points more than the percentage
of female voters who plan to vote Republican. Use the traditional method of hypothesis testing and use a
significance level of 0.05. Men: $\mathrm { n } _ { 1 } = 250 , \mathrm { x } _ { 1 } = 146$
Women: $\mathrm { n } _ { 2 } = 202 , \mathrm { x } _ { 2 } = 103$

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Definitions:

Dependent Means

Refers to the average outcomes within groups that are related or paired, often used in the analysis of experiments or studies.

Individuals

Refers to distinct objects or entities being studied or observed in research or statistical analysis, often representing people, animals, or units in an experiment or survey.

Null Hypothesis

The presumption in statistical testing that there is no significant effect or difference, serving as the default position until evidence suggests otherwise.

Dependent Means

A statistical term often used in the context of comparing two sets of related or matched data to determine if there's a significant difference between them.