To Test the Null Hypothesis That the Difference Between Two

question 32

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:

Coercive Power

The ability of a person to compel or force someone else to act in a certain way through threats, punishment, or control measures.

Withhold Positive Outcomes

The act of not presenting or delaying favorable results or benefits.

Behaviour

The manner in which an individual acts or conducts themselves, especially towards others.

Personal Integrity

The quality of being honest and having strong moral principles that one refuses to violate.