Question

When treating carpal tunnel syndrome, should a patient be treated with surgery or should a splint be applied? In a study on this issue, 73 patients were treated with surgery and 83 were treated with a splint. After 12 months, success was noted in 67 patients that had surgery, whereas success was noted in only 60 of the patients that had a splint. Assume that the observations came from a SRS.

a) (3 points) Construct an appropriate graphical summary to represent the number of failures for both groups.

b) (2 Points) Determine the risk of failure in the splint group.

c) (5 Points) Determine the odds ratio of failure   for the splint group compared to the surgery group. Interpret this odds ratio.

d) (5 points) Construct and interpret a 92% confidence interval for the true proportion of failure for the surgery group.

e) (10 Points) Use a 4% significance level to test if proportion of failure in the splint group is higher than the surgery group. (Define the parameter(s), state the hypotheses, specify α, compute the value of the test statistic and the p-value, and state your decision and conclusion in the context of the study.)

Answer 1

a)

1- surgery

2- splint

b)

p^= X/n = 23/83 = 0.2771

c)

odds ratio = (23/60)/ (6/(73-6) ) = 4 .2806

d)

92% confidence interval for failure

(-0.3155,-0.0743)

e)

Ho :p1 = p2

Ha: p1 < p2

TS = -3.12

p-value for left-tail = 0.001   < alpha (0.04)

hence we reject the null hypothesis

there is sufficient evidence that proportion of failure in the splint group is higher than the surgery group.

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