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.

(a) Describe carefully how to use slips of paper containing the sample data to generate one bootstrap statistic. In particular, how many slips of paper are needed and what is on them? What do we do with them to obtain a bootstrap sample? What statistic do we then record?

(b) Find and interpret a 95% confidence interval for the time immobile in a forced-swim test for mice receiving a shot of ketamine.

(c) Researchers report that the average immobile time for depressed mice is about 160 seconds. Based on the interval in part (b), is 160 a plausible value for the mean immobile time for mice treated with ketamine?