Would you favor spending more federal tax money on the arts? Of a random sample of n1 = 204 women, r1 = 70 responded yes. Another random sample of n2 = 178 men showed that r2 = 48 responded yes. Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts? Use ? = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: p1 = p2; H1: p1 > p2H0: p1 = p2; H1: p1 < p2 H0: p1 = p2; H1: p1 ≠ p2H0: p1 < p2; H1: p1 = p2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume the population distributions are approximately normal.The Student's t. The number of trials is sufficiently large. The standard normal. The number of trials is sufficiently large.The Student's t. We assume the population distributions are approximately normal. What is the value of the sample test statistic? (Test the difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.

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Description: Would you favor spending more federal tax money on the arts? Of a random sample of n1 = 204 women, r1 = 70 responded yes. Another random sample of n2 = 178 men showed that r2 = 48 responded yes. Does this information indicate a difference (either way

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

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Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 204 women, r₁ = 70 responded yes. Another random sample of n₂ = 178 men showed that r₂ = 48 responded yes. Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts? Use ? = 0.05.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: p₁ = p₂; H₁: p₁ > p₂H₀: p₁ = p₂; H₁: p₁ < p₂ H₀: p₁ = p₂; H₁: p₁ ≠ p₂H₀: p₁ < p₂; H₁: p₁ = p₂

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume the population distributions are approximately normal.The Student's t. The number of trials is sufficiently large. The standard normal. The number of trials is sufficiently large.The Student's t. We assume the population distributions are approximately normal.

What is the value of the sample test statistic? (Test the difference p₁ − p₂. Do not use rounded values. Round your final answer to two decimal places.)

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

Expert Solution

Step 1

Note: As per the guidelines, solution to only 3 subparts are provided.

Given information:

Sample size of women $(n_{1}) = 204$

Number of women who responded yes $(X_{1}) = 70$

Sample size of men $(n_{2}) = 178$

Number of men who responded yes $(X_{1}) = 48$

$α = 0.05$

Step 2

(a)

Level of significance is:

$α = 0.05$

The sample proportions can be calculated as follows:

$\begin{array}{rcl} {\hat{p}}_{1} & = & \frac{X_{1}}{n_{1}} \\ = & \frac{70}{204} \\ = & 0.3431 \\ {\hat{p}}_{2} & = & \frac{X_{2}}{n_{2}} \\ = & \frac{48}{178} \\ = & 0.2697 \end{array}$

The pooled proportion can be calculated as follows:

$\begin{array}{rcl} \bar{p} & = & \frac{X_{1} + X_{2}}{n_{1} + n_{2}} \\ = & \frac{70 + 48}{204 + 178} \\ = & 0.3089 \end{array}$

The hypotheses can be defined as follows:

$H_{0} : p_{1} = p_{2} H_{1} : p_{1} \neq p_{2}$

This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted.

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