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). Suppose for all face-to-face meetings in March 2020 the mean meeting time was 48.7 minutes with a standard deviation of 9.1 minutes. Additionally, suppose for all Zoom meetings in March 2020 the mean meeting time was 49.2 minutes with a standard deviation of 9.8 minutes. If a simple random sample of 62 face-to-face meetings in March 2020 is selected and stack X subscript 1 with bar on top= the mean length of this sample of 62 face-to-face meetings determined, and if an independent simple random sample of 66 Zoom meetings in March 2020 is selected and stack X subscript 2 with bar on top= the mean length of this sample of 66 Zoom meetings determined, if appropriate describe completely the sampling distribution of stack X subscript 1 with bar on top minus stack X subscript 2 with bar on top .

(b). Consider the sampling distribution determined in part (a). What is the probability that stack X subscript 1 with bar on top minus stack X subscript 2 with bar on top will be less than 0 minutes?

Answer 1

Given that

(a)

Since sampe sizes are large, that is greater than 30 so using central limit theorem we can assume that sampling distribtuion of difference in sample means will be approximately normal with following parameters:

(a)

The z-score for is

Using z table, the required probability is

Answer: 0.6179