How often do you go out dancing? This question was asked by a professional survey group on behalf of the National Arts Survey. A random sample of n1 = 97 single men showed that r1 = 24 went out dancing occasionally. Another random sample of n2 = 91 single women showed that r2 = 18 went out dancing occasionally. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. (a) Do these data indicate that the proportion of single men who go out dancing occasionally is higher than the proportion of single women who do so? Use a 5% level of significance. List the assumptions you made in solving this problem. Do you think these assumptions are realistic? (i) What is the level of significance? What is the value of the sample test statistic? (Round your answer to three decimal places.) (b) Compute a 90% confidence interval for the population difference of proportions p1 − p2 of single men and single women who occasionally go out dancing. (Round your answers to three decimal places.) lower limit upper limit

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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How often do you go out dancing? This question was asked by a professional survey group on behalf of the National Arts Survey. A random sample of

n₁ = 97

single men showed that

r₁ = 24

went out dancing occasionally. Another random sample of

n₂ = 91

single women showed that

r₂ = 18

went out dancing occasionally. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer.

(a) Do these data indicate that the proportion of single men who go out dancing occasionally is higher than the proportion of single women who do so? Use a 5% level of significance. List the assumptions you made in solving this problem. Do you think these assumptions are realistic?

(i) What is the level of significance?

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(b) Compute a 90% confidence interval for the population difference of proportions

p₁ − p₂

of single men and single women who occasionally go out dancing. (Round your answers to three decimal places.)

lower limit
upper limit

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