(a) We would like to estimate the true proportion p of all Winnipeg drivers who
ID: 3150659 • Letter: #
Question
(a) We would like to estimate the true proportion p of all Winnipeg drivers who have received a speeding ticket. A random sample of Winnipeg drivers is selected, and a 99% confidence interval for p is calculated to be (0.63, 0.72). Provide an interpretation of this confidence interval.
(b) We would like to conduct a hypothesis test to determine whether there is evidence that the unemployment rates in the United States and Canada differ. In a random sample of Americans, 9% are found to be unemployed. In a random sample of Canadians, 8% are found to be unemployed. A hypothesis test is conducted, and the P-value is calculated to be 0.2460. Provide an interpretation of this P-value.
Explanation / Answer
a) We are given that we would like to estimate the true proportion p of all Winnipeg drivers who have received a speeding ticket. A random sample of Winnipeg drivers is selected, and a 99% confidence interval for p is calculated to be (0.63, 0.72).
Interpretation : We are 99% confident that the true population proportion is in between 0.63 and 0.72.
b) Here we have to test the hypothesis that,
H0 : p1 = p2 Vs H1 : p1 p2
where p1 is population proportion of unemployment rates in the United States.
p2 is the population proportion of unemployment rates in the Canada.
Assume alpha = level of significance = 5% = 0.05
p1^ = sample proportion of unemployment rates in the United States = 9% = 0.09
p2^ = sample proportion of unemployment rates in the Canada = 8% = 0.08
Given that P-value = 0.2460
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : Population proportion of unemployment rates in the United States and population proportion of unemployment rates in the Canada are equal.
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