Would you favor spending more federal tax money on the arts? Of a random sample of n1 = 225 women, r1 = 68 responded yes. Another random sample of n2 = 162 men showed that r2 = 64 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 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.The standard normal. 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.

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

Problem 8CR

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Question

Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 225 women, r₁ = 68 responded yes. Another random sample of n₂ = 162 men showed that r₂ = 64 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 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.The standard normal. 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.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.Reject the null hypothesis, there is sufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men. Fail to reject the null hypothesis, there is insufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.Reject the null hypothesis, there is insufficient evidence that the proportion of women favoring more tax dollars for the arts is different from the proportion of men.

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