Would you favor spending more federal tax money on the arts? Of a random sample of n1 = 87 politically conservative voters, r1 = 20 responded yes. Another random sample of n2 = 78 politically moderate voters showed that r2 = 21 responded yes. Does this information indicate that the population proportion of conservative voters inclined to spend more federal tax money on funding the arts is less than the proportion of moderate voters so inclined? Use α = 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 Student's t. We assume the population distributions are approximately normal. The standard normal. The number of trials is sufficiently large.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.)

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Description: Would you favor spending more federal tax money on the arts? Of a random sample of n1 = 87 politically conservative voters, r1 = 20 responded yes. Another random sample of n2 = 78 politically moderate voters showed that r2 = 21 responded yes. Does th

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 87 politically conservative voters, r₁ = 20 responded yes. Another random sample of n₂ = 78 politically moderate voters showed that r₂ = 21 responded yes. Does this information indicate that the population proportion of conservative voters inclined to spend more federal tax money on funding the arts is less than the proportion of moderate voters so inclined? Use α = 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 Student's t. We assume the population distributions are approximately normal. The standard normal. The number of trials is sufficiently large.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.)

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