Question

Interpreting Displays.

In Exercises 5 and 6, use the results from the given displays.

Treating Carpal Tunnel Syndrome Carpal tunnel syndrome is a common wrist complaintresulting from a compressed nerve, and it is often the result of extended use of repetitive wristmovements, such as those associated with the use of a keyboard. In a randomized controlledtrial, 73 patients were treated with surgery and 67 were found to have successful treatments.Among 83 patients treated with splints, 60 were found to have successful treatments (based ondata from “Splinting vs Surgery in the Treatment of Carpal Tunnel Syndrome,” by Gerritsenet al., Journal of the American Medical Association, Vol. 288, No. 10). Use the accompanyingStatCrunch display with a 0.01 significance level to test the claim that the success rate is better with surgery.

Short answer

There is sufficient evidence to support the claim that the success rate for surgery is better than the success rate of splints in the treatment at a 0.01 level of significance.

Step-by-step solution

Given information

The output is known

Describe the hypothesis to be tested

Let\({p_1}\)be the population proportion of success rate in splinting and\({p_2}\)be population proportion of success rate in surgery.

Mathematically, the test hypothesis is,

\(\begin{array}{l}{H_0}:{p_1} = {p_2}{\rm{ }}\\{H_1}:{p_1} < {p_2}\end{array}\)

The test is one-tailed.

State the result

The decision rule:

If p value is less than the level of significance then reject the null hypothesis at\({\rm{\alpha }}\)level of significance.

Here, the p-value is 0.0009 which is less than the level of significance\(\alpha = 0.01\).

Therefore, reject null hypothesis at 0.01significance level.

Interpret the result

Therefore, there is sufficient evidence to support the claim that the success rate for surgery is better than the success rate of splinting.