Question

The data to the right show the average retirement ages for a random sample of workers...

The data to the right show the average retirement ages for a random sample of workers in Country A and a random sample of workers in Country B. Complete parts a and b.

   Country A Country B

Sample mean 63.4 years    65.2 years

Sample size 40 40

Population standard deviation 4.3 years 5.4 years

a. Perform a hypothesis test using alpha α = 0.01 to determine if the average retirement age in Country B is higher than it is in Country A.

Let population 1 be the workers in Country A and population 2 be the workers in Country B. Identify the null and alternative hypotheses. Choose the correct answer below.

A. H0​: μ1 − μ2 <0

H1​: μ1-μ2 ≥0

B. H0​: μ1 − μ2 ≠0

   H1​: μ1 − μ2 =0

C. H0​: μ1 − μ2 ≥0

   H1​: μ1 − μ2 <0

D. H0: μ1−μ2≤0

   H1: μ1−μ2>0

E. H0​: μ1 − μ2 >0

H1​: μ1 − μ2 ≤0

F. H0​: μ1 − μ2 =0

H1: μ1 − μ2 ≠0

Calculate the appropriate test statistic.

The test statistic is . ​(Round to two decimal places as​ needed.)

Determine the appropriate critical​ value(s). The critical​ value(s) is(are) . ​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)

Since the test statistic ▼ falls/does not fall in the rejection​ region, ▼ do not reject/reject H0. There is ▼ sufficient/insufficient evidence to conclude that the average retirement age in Country B is higher than it is in Country A.

b. Determine the​ p-value and interpret the results. The​ p-value is . ​(Round to three decimal places as​ needed.) Since the​ p-value is ▼ equal to/less than/greater than α​, ▼ do not reject/reject H0. There is ▼ sufficient/insufficient evidence to conclude that the average retirement age in Country B is higher than it is in Country A.

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