A researcher is looking at the effect of a new therapy for i

A researcher is looking at the effect of a new therapy for improving range of motion (ROM) after shoulder surgery. She recruits a sample of eleven patients who underwent surgery in the previous six months, and measures ROM at baseline and again after six weeks of therapy. The data appear below:

Patient 1 2 3 4 5 6 7 8 9 10 11

Baseline 14º 12º 11º 18º 4º 5º 11º 13º 10º 12º 12º

6 weeks 16º 11º 10º 22º 11º 15º 18º 11º 10º 13º 17º

The researcher is concerned that there may be a confounding factor in her study, specifically the fact that the patients she recruited may not be particularly representative of the population of all shoulder surgery patients. According to recent findings in the American Journal of Rehabilitation Medicine, the mean ROM for patients after surgery is 10º.

a. Which test is appropriate for answering the question: Is the mean ROM at baseline for these patients different from 10º?

b. For the test you specified in (a), formally state the null and alternative hypotheses.

c. What are your assumptions for this test?

d. Looking at the test statistic for the test you specified in (a), what is the distribution of this statistic if the null hypothesis is true?

e. Calculate the test statistic and the corresponding p-value. f. What do you conclude at a 0.05 significance level?

Solution