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 standard deviation of the number of people attending all Zoom meetings in March 2020 is 7.1, and that the standard deviation of the number of people attending all face-to-face meetings in March 2020 is 6.5. A simple random sample of 96 Zoom meetings from March 2020 was selected, and the mean number of people attending this sample of 96 meetings was 22.1. An independent simple random sample of 61 face-to-face meetings in March 2020 was selected, and the mean number of people attending this sample of 61 meetings was 19.3. If appropriate, use this information to calculate and interpret a 95% 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.

Answer 1

Sample 1 Sample 2 Sample Population Sample Size mean S.D ng = 96 X2 = 22.1 | 01 = 7.1 n2 = 61X2 = 19.3 02 =6.5 Standard Error = 101O = sqrt[(7.12/96)+(6.52/61)] = 1.1035 V n n2 Confidence Level = 95 Significance Level = a = (100-95)% = 0.05 Critical value = z* = 1.96 [Using Excel =ABS(NORMINV(/2,0,1))] Margin of Error = z* (standard error )= 1.96*1.1035 = 2.16287 Lower Limit = (21-22 )- Margin of Error = (22.1 - 19.3) - 2.16287 = 0.6371 Upper Limit = (X1-82 )+ Margin of Error = (22.1 - 19.3) + 2.16287 = 4.9629 Ans:(0.6371, 4.9629)

Interpretation:

We are 95% confident that the true mean 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 is lies between 0.6371 and 4.9629.