Exercise B.33 describes a study on the use of ketamine in treating depression in mice. Ten depressed mice given the drug had a mean score of 135 seconds on a forced-swim test used to measure depression (lower scores indicate less depression). The usual mean for depressed mice on this test is about 160 seconds.

(a) Using the parameter μ to denote the mean score on this test for depressed mice after treatment with ketamine, what are the null and alternative hypotheses for seeing if there is evidence that the mean score is lower than 160?

(b) Describe carefully how to use slips of paper to generate one randomization statistic for this test. In particular, how many slips of paper are needed and what do we write on them? What do we do with them to obtain a randomization sample? What statistic do we then record?  

Exercise B.33

Traditional antidepressants often take weeks or months to improve symptoms. A new study may provide a faster acting option. The anesthetic ketamine is very dangerous and can be deadly at high doses. However, low doses appear to have a rapid effect on levels of a brain compound linked to depression. In the study, mice receiving a single injection of ketamine showed fewer signs of depression within 30 minutes and the results lasted almost a week. One standard test of depression in mice is called the forced-swim test: Mice who are not depressed will struggle longer to stay afloat rather than giving up and sinking. The quantity measured is seconds that the mouse is immobilized, and lower numbers mean less depression. In a sample of 10 depressed mice 30 minutes after receiving a shot of ketamine, the mean number of seconds immobile was 135 with a standard error for the estimate of 6.