Question

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 = 98 single men showed that r1 = 24 went out dancing occasionally. Another random sample of n2 = 93 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? State the null and alternate hypotheses. H0: p1 = p2; H1: p1 < p2 H0: p1 < p2; H1: p1 = p2 H0: p1 = p2; H1: p1 > p2 H0: p1 = p2; H1: p1 ≠ p2 (ii) What sampling distribution will you use? What assumptions are you making? 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. The Student's t. The number of trials is sufficiently large. What is the value of the sample test statistic? (Round your answer to three decimal places.) (iii) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (v) Interpret your conclusion in the context of the application. There is sufficient evidence at the 0.05 level to conclude that the population proportion of single men is greater than the population proportion of single women. There is insufficient evidence at the 0.05 level to conclude that the population proportion of single men is greater than the population proportion of single women. (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

Answer 1

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