Knowledge of the amount of time a patient occupies a hospital bed—called length of stay (LOS)—is important for allocating resources. At one hospital, the mean LOS was determined to be 5 days. A hospital administrator believes the mean LOS may now be less than 5 days due to a newly adopted managed health care system. To check this, the LOSs (in days) for 100 randomly selected hospital patients were recorded; these data are listed in Table 7.4. Suppose we want to test the hypothesis that the true mean length of stay at the hospital is less than 5 days; that is,

Assuming that σ = 3.68, use the data in the table to conduct the test at α = .05.

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Ho: μ = 5(Mean LOS after adoption is 5 days) H₂: μ< 5 (Mean LOS after adoption is less than 5 days)