Question

please do this correctly and if you could please write out any formulas and show work as much as possible.

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7) A sample survey is designed to estimate the proportion of sports utility vehicles and minivans being driven in the state of California. A random sample of 500 registrations is selected from a DMV database. 68 are classified as sports utility vehicles and 84 are classified as minivans. Is there evidence to suggest a difference in the proportion of sports utility vehicles and the proportion of minivans in California, with a confidence level of 97.5%? Justify your answer.

Answer 1

Null hypothesis: Ho: P = P2 There is no difference in the proportion of sports utility vehicles and the proportion of minivans in California Alternative hypothesis: H:POP2 There is a difference in the proportion of sports utility vehicles and the proportion of minivans in Califomia. Rejection rule: If p-values a(=0.025), then reject the null hypothesis H. EXCEL (Mega Stat) output:

Hypothesis test for two independent proportions p1 0.136 68/500 68. 500 p2 0.168 84/500 84. 500 Po 0.152 p (as decimal) 152/1000 p (as fraction) 152. X 1000 n -0.032 difference 0. hypothesized difference 0.0227 std. error -1.41 z .1587 p-value (two-tailed) Test Statistic: z=-1.41. P-value = 0.1587. Conclusion: Use a significance level, a = 0.025. Here, p-value is 0.1587, which is greater than the value of a = 0.025. That is, p-value (= 0.1587) > a{=0.025). Therefore, by the rejection rule, do not reject the null hypothesis Ho-

Interpretation: There is insufficient evidence at level of significance a = 0.025. There is no difference in the proportion of sports utility vehicles and the proportion of minivans in California.