Question

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 mean number of people attending all Zoom meetings in March 2020 is 23.4 with a standard deviation of 7.5, and that the mean number of people attending all face-to-face meetings in March 2020 is 22.7 with a standard deviation of 6.8. If a simple random sample of 9 Zoom meetings in March 2020 is selected and top enclose X subscript 1 end enclose = the mean number of people attending this sample of 9 Zoom meetings determined, and if an independent simple random sample of 13 face-to-face meetings in March 2020 is selected and stack X subscript 2 with bar on top the mean number of people attending this sample of 13 face-to-face meetings determined, if appropriate describe completely the sampling distribution of .

Answer 1

Since we know population sd , distribution follow normal distribution

Xba1r- Xbar2 follow

standard normal distribution with

mean = 23.4 - 22.7 =

sd =sqrt(7.5^2/9 + 6.8^2/13)= 3.1316