14. (0.5 + 0.5 + 1 + 1 + 1 = 4 marks) An experiment was conducted to compare the mean time (in days) to recover from a viral infection for people given a daily dose of a new drug versus those who were not given a new drug. The average recovery time for the treated group of 10 people was 4.7 days with the standard deviation of 0.92 days. The average recovery time for non treated group of 10 people was 5.1 days with the standard deviation of 1.20 days Test appropriate hypothesis at a = 0.05 using critical value approach. The data summary is given in the table below. Treated group Untreated group 1 = 10 12 = 10 X = 4.7 X, =5.1 $1 = 0.92 $2 = 1.20 Assume that populations of recovery times for treated people and for untreated people are both normal. Assume that population variances may be assumed equal and common population variance is estimated with the value of pooled sample variance. Do the data provide sufficient sample evidence to indicate that mean recovery time for treated people is smaller than mean recovery time for untreated people? Test appropriate hypotheses. Use a = 0.05 . a. State null and research hypotheses about the difference in mean recovery times. H : H, : a. State the value of pooled sample variance. Keep three digits after decimal point in the answer. The value of pooled sample variance is S= =b. State the observed value of test statistic Keep three digits after decimal point in the answer. The observed value of test statistic is t obs. = C. The rejection region is d. Insert the word sufficient or insufficient into the following statement. There is sample evidence to conclude that the mean recovery time for treated people is smaller than the mean recovery time for untreated people