Homework SourseProblem 8 Researchers interviewed young adults in Canada and
(Problem 8) Researchers interviewed young adults in Canada and the U.S to compare their ages when they enter the workforce. The mean age of the 100 Canadians was 18 with a standard deviation of 6. The mean age of the 130 people interviewed in the U.S. was 20 with a standard deviation of 8. Is the mean age of entering the workforce in Canada lower than the mean age in the U.S.? (5 points each, 15 points total)
(a) Identify the null and alternate hypothesis
(b) Find the test statistic (show all work).
(c) Find the P-value (show all work) and evaluate whether the mean age of entering the workforce in Canada is lower than the mean age in the U.S.? Test at a 1% significance level.
Solution
Let group 1 = canadians
group 2 = americans.
Formulating the null and alternative hypotheses,
Ho: u1 - u2 >= 0
Ha: u1 - u2 < 0 [ANSWER, PART A]
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At level of significance = 0.01
As we can see, this is a left tailed test.
Calculating the means of each group,
X1 = 18
X2 = 6
Calculating the standard deviations of each group,
s1 = 20
s2 = 8
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 100
n2 = sample size of group 2 = 130
Thus, df = n1 + n2 - 2 = 228
Also, sD = 2.119506474
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = 5.661695375 [ANSWER, TEST STATISTIC]
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c)
where uD = hypothesized difference = 0
Also, using p values, as df = 228,
p = 2.24233*10^-8
Comparing this to the significance level, WE REJECT THE NULL HYPOTHESIS.
Thus, there is sufficient evidence that the mean age of entering the workforce in Canada is lower than the mean age in the U.S. [CONCLUSION]
