In: Statistics and Probability
(a). Now the population is all senior living facilities in the United States. It is conjectured that the mean number of positive COVID-19 cases per 100 residents is 40, and of interest is to test this conjecture versus the alternative that the mean number of positive COVID-19 cases per 100 residents is different from 40. State the appropriate null and alternative hypotheses that should be tested.
(b). Consider the information and hypotheses specified in part (a). A simple random sample of 61 senior living facilities in the United States was selected and the mean number of positive COVID-19 cases per 100 residents was recorded for each. The mean number of positive COVID-19 cases per 100 residents in this sample of 61 senior living facilities was 43.2, with a standard deviation of 8.7. If appropriate, use this information to test the hypotheses stated in part (a) at the a = .05 level of significance.