A researcher in an alcoholism treatment center, to study the length of stay in the center for first-time patients, randomly selects 10 records of individuals institutionalized within the previous two years. The lengths of stay, in days, were 11, 6, 20, 9, 13, 4, 39, 13, 44, and 7. For a similar study 25 years ago, lengths of stay, in days, for 10 sampled individuals were 32, 18, 55, 17, 24, 31, 20, 40, 24, and 15.

Software shows results:

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Variable | Obs Mean Std. Dev. Min Max stay_new | 10 16.6 13.91402 4 44 stay_old | 10 27.6 12.39355 15 55

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(a) Summarize results in the two studies, using measures of center and variability. Interpret any differences you find.

(b) Actually, the new study also selected one other record.

That patient is still institutionalized after 40 days. Thus, that patient’s length of stay is at least 40 days, but the actual value is unknown. Can you calculate the mean or median for the complete sample of size 11 including this partial observation? Explain. (This observation is said to be censored, meaning that the observed value is “cut short”

of its true, unknown value.)