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 83 face-to-face meetings held in March 2020 was selected, and the mean length of this sample of 83 meetings was 46 minutes with a standard deviation of 13.6 minutes. An independent simple random sample of 81 Zoom meetings held in March 2020 was selected, and the mean length of this sample of 81 meetings was 51 minutes with a standard deviation of 11.6 minutes. If appropriate, use this information to test the hypotheses stated in part (a) at the alpha = .10 level of significance.

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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...

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...

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