Question

1) 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; Suppose we want to test the hypothesis that the true mean length of stay at the hospital is less than 5 days; 2 3 8 6 4 4 6 4 2 5 8 10 4 4 4 2 1 3 2 10 1 3 2 3 4 3 5 2 4 1 2 9 1 7 17 4 9 9 9 4 1 1 1 3 1 6 3 3 2 5 1 3 3 14 2 3 9 6 6 3 5 1 4 6 11 22 1 9 6 5 2 2 5 4 6 3 1 5 1 6 17 1 2 4 5 4 4 3 2 3 3 5 2 3 3 2 10 2 4 2

Answer 1

level of significance, ? = 0.05

sample size, n = 100

sample mean,xbar=4.53 (sum of all observation/n)

population mean, ? = 5

sample standard deviation, s= 3.67

population standard deviation, sx = (s/ (n)1/2) = 0.367

FORMULATING THE HYPOTHESIS

• ?0: ? >= 5
• ??: ? < 5

here, we perform one-sample t-test ( a test of mean)

tcal=(xbar - ?) / sx = (4.53-5)/0.367 = -1.28

since, tcal/2=-0.64 & -0.64<1.96 , i.e, p-value>alpha

We FAIL to reject the ?0.

Thus, we have sufficient evidence to prove that LOS is less than 5 days.