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:

Behavior

Actions or reactions of an entity or organism, often in response to the environment, showcasing a broad spectrum of activity.

Stimulus

any object or event that elicits a sensory or behavioral response in an organism.

Probability

A mathematical measure of the likelihood of a particular event occurring, expressed as a number between 0 and 1.

Successive Approximations

A method in behavioral psychology where rewards are given for behaviors that increasingly resemble the target behavior.