28. An experiment has been devised to test the hypothesis that an elderly person’s memory retention can be improved by a set of “oxygen treatments.” A group of scientists administered these treatments to men and women. The men and women were each randomly divided into 4 groups of 5 each, and the people in the ith group were given treatments over an (i − 1) week interval, i = 1, 2, 3, 4. (The 2 groups not given any treatments served as “controls.”) The treatments were set up in such a manner that all individuals thought they were receiving the oxygen treatments for the total 3 weeks. After treatment ended, a memory retention test was administered. The results (with higher scores indicating higher memory retentions) are shown in the table.

(a) Test whether or not there is an interaction effect.

(b) Test the hypothesis that the length of treatment does not affect memory retention

(c) Is there a gender difference?

(d) A randomly chosen group of 5 elderly men, without receiving any oxygen treatment, were given the memory retention test. Their scores were 37, 35, 33, 39, 29. What conclusions can you draw?

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Scores Number of Weeks of Oxygen Treatment 0 1 2 3 Men 42 39 38 42 54 52 50 55 46 51 47 39 38 50 45 38 51 47 43 51 Women 49 48 27 61 44 51 42 55 50 52 47 45 45 54 53 40 43 40 58 42