Answered: Would you favor spending more federal…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 232 women, r₁ = 66 responded yes. Another random sample of n₂ = 198 men showed that r₂ = 65 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. We assume the population distributions are approximately normal.The standard normal. We assume the population distributions are approximately normal. The standard normal. The number of trials is sufficiently large.The Student's t. The number of trials is sufficiently large.

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 fail to 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 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. 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.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.

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