(a)The population is all VCU faculty, and of interest is to compare the mean number of Zoom meetings they attended in March 2020 to the mean number of face-to-face meetings they attended in March 2020. It is conjectured that the mean number of Zoom meetings in March 2020 and the mean number of face-to-face meetings in March 2020 attended by all VCU faculty are the same, and of interest is to test this conjecture versus the alternative that the two means are different. Based on this, state the appropriate null and alternative hypotheses that should be tested.
(b) A simple random sample of 12 VCU faculty was selected. Each of these 12 faculty was asked how many Zoom meetings they attended in March 2020, and how many face-to-face meetings they attended in March 2020. For each faculty member the difference in the number of Zoom and face-to-face meetings was determined. The mean of this sample of 12 differences was 2.9, with a standard deviation of 4.4. It is known that the distribution of all such differences is normally distributed. If appropriate, use this information to test the hypotheses stated in part (a) at the α = .05 level of significance.
Solution: The null and alternative hypotheses are:
Under the null hypothesis, the test statistic is:
Conclusion: Since the p-value is less than the significance level, we, therefore, reject the null hypothesis and conclude that the mean differences are statistically significant.
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