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

question 34

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 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: $\mathrm { n } _ { 1 } = 250 , \mathrm { x } _ { 1 } = 146$
Women: $n _ { 2 } = 202 , x _ { 2 } = 103$

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Definitions:

Beta

A measure of a stock's volatility in relation to the overall market; a beta above 1 indicates that the stock is more volatile than the market, while a beta below 1 indicates it is less volatile.

Unadjusted Beta

Unadjusted beta is the raw beta value of a security or portfolio without any adjustments for its specific risks and characteristics, typically used as a measure of its volatility against the market.

Adjusted Betas

Betas that have been modified to account for the tendency of a stock's market risk measure to regress towards the mean over time, used in finance to predict future betas.

Market Index

A statistical aggregate that measures the performance of a basket of stocks to represent a particular market or sector.