In: Statistics and Probability
Suppose the first population is all Zoom meetings held in March 2020, the second population is all face-to-face meetings held in March 2020, and the parameter of interest is μ1 – μ2 = the difference in the mean number of people attending all Zoom meetings and the mean number of people attending all face-to-face meetings. For both Zoom meetings and face-to-face meetings the distributions are skewed heavily to the right due to some meetings that have many people in attendance.
It is known that the standard deviation of the number of people attending all Zoom meetings in March 2020 is 7.5, and that the standard deviation of the number of people attending all face-to-face meetings in March 2020 is 6.8. A simple random sample of 84 Zoom meetings from March 2020 was selected, and the mean number of people attending this sample of 84 meetings was 21.6. An independent simple random sample of 51 face-to-face meetings in March 2020 was selected, and the mean number of people attending this sample of 51 meetings was 17.4. If appropriate, use this information to calculate and interpret a 99% confidence interval for the difference in the mean number of people attending all Zoom meetings in March 2020 and the mean number of people attending all face-to-face meetings in March 2020.