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:

Single Gene

Refers to a trait or condition determined by a single gene in an organism's genome.

DNA

Deoxyribonucleic acid, the self-replicating material present in nearly all living organisms, serving as the carrier of genetic information.

Base Pairs

The pairs of nucleotides (adenine with thymine, and cytosine with guanine) that form the rungs of the DNA double helix, essential for coding genetic information.

DNA Molecule

A DNA molecule is a complex, double-helical structure carrying the genetic information necessary for an organism's growth, development, functioning, and reproduction.