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:

Window of Vulnerability

A critical period in which an individual is more susceptible to specific negative influences or harm, often due to transition or particular developmental stages.

Andrew Wakefield

A discredited former British doctor known for his fraudulent study suggesting a link between the MMR vaccine and autism, leading to a major public health scare.

MMR Vaccine

A vaccine designed to protect against measles, mumps, and rubella, three highly infectious diseases.

Window of Vulnerability Model

A concept in public health and psychology that identifies periods when individuals are more susceptible to certain risks or influences.