Question

Typically, elderly patients with hip fractures may have long recovery times. At one hospital, the average amount of time that elderly patients with hip fractures would spend in the hospital before they could be released to home care was 15 days. A new physiotherapy program is developed and researchers want to see if this new program gives recovery times that are different than the typical average amount. A random sample of 12 patients was enrolled in the new program and the amount of time each patient spent in hospital (measured in days) is recorded below.

10 9 11 10 8 9 15 17 20 11 7 12

If needed, assume that the number of hospital care days required follows the normal distribution.

a) Define the parameter of interest using the correct notation. Then, state the null and alternative hypotheses for this study.

b) Calculate the observed value of the test statistic. State the distribution (and degrees of freedom if needed) it follows. 2

c) Compute the p-value or provide a range of appropriate values for the p-value.

d) Using the significance level α = 0.05, state your conclusion for the study.

e) What type of error (Type I or Type II) might have been made here due to your conclusion in part (d)? Explain.

(f) Suppose that the researchers intend to use the hospital time data from these 12 patients as a pilot study for a much larger study in the future. If one of their goals is to construct a 95% confidence interval for the true mean hospital time needed after a hip fracture, to within 0.5 days, what sample size would they require? (Give your answer as a whole number)

Answer 1