A researcher claims that New Zealanders spend more time exercising than Australians. The researcher takes a random sample of 41 New Zealanders and finds that they spend an average of 130 minutes per day exercising, with a standard deviation of 24. A sample of 61 Australians averaged 110 minutes a day of exercise, with a standard deviation of 16.
a) Assuming equal variances, test the claim that New Zealanders exercise more than Australians at the 0.05 significance level.
b) Assuming unequal variances, repeat the test at the 0.05 significance level.
c) Test whether the variances are equal at the 0.05 significance level.
d) Based on your answer to part c), which was the appropriate test for the means (a), or b))? Give reasons for your answer.
e) Explain the unequal variances problem and its relevance, if any, to your conclusions about whether New Zealanders exercise more than Australians.