Question

A random sample of n1 = 290 voters registered in the state of California showed that 143 voted in the last general election. A random sample of n2 = 216 registered voters in the state of Colorado showed that 130 voted in the most recent general election. Do these data indicate that the population proportion of voter turnout in Colorado is higher than that in California? Use a 5% level of significance. (a) 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 (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 Student's t. The number of trials is sufficiently large. The standard normal. We assume the population distributions are approximately normal. The standard normal. 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. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (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 α? 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. 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 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 insufficient evidence that the proportion of voter turnout in Colorado is greater than that in California. Reject the null hypothesis, there is sufficient evidence that the proportion of voter turnout in Colorado is greater than that in California. Fail to reject the null hypothesis, there is sufficient evidence that the proportion of voter turnout in Colorado is greater than that in California. Reject the null hypothesis, there is insufficient evidence that the proportion of voter turnout in Colorado is greater than that in California.

Answer 1

A) The level of significance is 0.05.

H₀: P1 = P2

H₁: P1 < P2

b) The standard normal.The number of trials is sufficiently large.

= 143/290 = 0.4931

= 130/216 = 0.6019

The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2)

                                                     = (0.4931 * 290 + 0.6019 * 216)/(290 + 216) = 0.5395

The test statistic z = ()/sqrt(P(1 - P)(1/n1 + 1/n2))

                             = (0.4931 - 0.6019)/sqrt(0.5395 * (1 - 0.5395) * (1/290 + 1/216))

                             = -2.43

c) P-value = 2 * P(Z < -2.43)

                 = 2 * 0.0075

                 = 0.0150

Since the P-value is less than the significance level (0.0150 < 0.05), so we should reject the null hypothesis.

At the alpha = 0.05 level, we reject the null hypothesis and conclude that the data are statistically significant.

e) Reject the null hypothesis, there is sufficient evidence that the proportion of voter turnout in Colorado is greater than that in California.