Question

Problem 2. (15pts) A hospital performs a study to investigate the effect of a new medicine on the number of days it takes patients to recover from surgery. Twelve patients are divided at random into two groups of six each. The first group is treated as usual, while the second group is treated with the new medicine. For the first group, the recovery times had a mean of 14.8 days and a variance of 3.9; for the second group, the recovery times had a mean of 12.9 days and a variance of 3.3. Assume that the populations of recovery times under both treatments have normal distributions with equal standard deviations and that the two samples are independent. (1) Set up the null and alternative hypotheses to test if the new medicine reduced the recovery time after surgery. a) Ho: Mi - H2 = 0 vs. H: Mi - H2 + 0 b) Ho: Mi- 2 > 0 vs. H: Mi - H2 < 0 c) H0 : Mi - M2 >.9 vs. Hi : Mi - M2 <.9 d) HO : M - M2 < 0 vs. H: Mi - H2 > 0 (2) The value of the test statistic is a) 0.98 b) 1.73 c)-1.86 d) 1.72 e) 0.77 (3) What is the rejection region for the test at a = 0.1? a) t > 1.37 b) < -1.37 or 2 > 1.37 c) d) t > 1.81 e) z < -1.64 < -1.81 (4) Find a 90% confidence interval for the difference Mi - uz of the mean number of days it takes patients to recover from surgery under the two medicines. a) 0.9 3.70 b) 1.9 2.36 c)-1.9 2.36 d) 1.9 +1.99 e) 0.9 +1.05

Answer 1

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