Question

Suppose the first population is all face-to-face meetings held in March 2020, the second population is all Zoom meetings held in March 2020, and the parameter of interest is μ₁ – μ₂ = the difference in the mean length of all face-to-face meetings and the mean length of all Zoom meetings. The meeting lengths are measured in minutes. For both face-to-face meetings and Zoom meetings the distributions of meeting times are skewed heavily to the right due to some meetings that are very long.

       (a). Of interest is to test the hypothesis that the mean length of all face-to-face meetings and the mean length of all Zoom meetings are the same, versus the alternative hypothesis that the mean length of all face-to-face meetings is less than the mean length of all Zoom meetings. State the appropriate null and alternative hypotheses that should be tested.

       (b). A simple random sample of 47 face-to-face meetings held in March 2020 was selected, and the mean length of this sample of 47 meetings was 51 minutes with a standard deviation of 15.6 minutes. An independent simple random sample of 41 Zoom meetings held in March 2020 was selected, and the mean length of this sample of 41 meetings was 54 minutes with a standard deviation of 14.0 minutes. If appropriate, use this information to test the hypotheses stated in part (a) at the α = .01 level of significance.

Answer 1

Solution: