Question

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 below.

Country A Country B

Sample mean 62.2 years 64.7 years

Sample size 40 40

Population standard deviation 4.1 years 5.2 years

part a.) Perform a hypothesis test using alphaαequals=0.05 to determine if the average retirement age in Country B is higher than it is in Country A.

part b.) what is the test statistic?

part c.) the critical value(s) are?

part d.) since the test statistic __________ in the rejection region, __________ H0. There is ___________ evidence to conclude that the average retirement age in Country B is higher than it is in Country A.

part e.) determine the p value

part f.) since the p value is _________ alpha __________ H0. There os _________ evidence to conclude that the average retirement age in Country B is higher than it is in Country A.

Answer 1

Sol:'since population standard deviations are known

Ho:mu1-mu2=0

mu1=mean of country B

mu2=mean of country B

Ha;mu1-mu2>0

alpha=0.05

Solution-b:

perform z test for difference in means

z=x1bar-x2bar/sqrt(sigma1^2/n1+igma2^2/n2)

z=(64.7-62.2)/sqrt(((5.2)^2/40+4.1^2/40)))

z= 2.38773

Solution-C:

the critical value is

=NORMINV(0.05,0,1)

=1.64485

the critical value is 1.64485

Solution-d:

part d.) since the test statistic lies  in the rejection region, Reject H0. There is suffcient evidence to conclude that the average retirement age in Country B is higher than it is in Country A.

Solution-e:

p value for right tail is

=1-NORM.S.DIST(2.38773,TRUE)

=1-0.991524

=0.008476

p=0.0085

part f.) since the p value is less than alpha reject H0. There is suffcient evidence to conclude that the average retirement age in Country B is higher than it is in Country A.