Question

Medical research has shown that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at Cornell University used a proposed new computer mouse design, and while using the mouse, each student's wrist extension was recorded. Data consistent with summary values given in the paper "Comparative Study of Two Computer Mouse Designs" (Cornell Human Factors Laboratory Technical Report RP7992) are given. Use these data to test the hypothesis that the mean wrist extension for people using this new mouse design is greater than 20 degrees. Are any assumptions required in order for it to be appropriate to generalize the results of your test to the population of all Cornell students? To the population of all university students? $$ \begin{array}{lllllll} 27 & 28 & 24 & 26 & 27 & 25 & 25 \\ 24 & 24 & 24 & 25 & 28 & 22 & 25 \\ 24 & 28 & 27 & 26 & 31 & 25 & 28 \\ 27 & 27 & 25 & & & & \end{array} $$

Short answer

The hypothesis can be tested using a one-sample t-test. If the p-value obtained is less than 0.05, the null hypothesis that the mean wrist extension is equal to 20 degrees is rejected in favor of the alternative hypothesis that the mean wrist extension is greater than 20 degrees. Assumptions need to be checked for this test, and generalizing the results to all Cornell students or all university students would require a representative sample.

Step-by-step solution

Compute the Mean

First, compute the sample mean of the wrist extension measurements. This can be found by adding all the measurements together and then dividing by the number of measurements.

Compute the Standard Deviation

Next, calculate the sample standard deviation. This is found by taking the square root of the variance, which is the average of squared differences from the mean.

Conduct a One-Sample t-test

Now, a one-sample t-test is conducted to test the hypothesis that the mean wrist extension is greater than 20 degrees. The null hypothesis is that the mean is equal to 20 degrees, while the alternative hypothesis is that the mean is greater than 20 degrees. A significance level of 0.05 is typically used.

Analyze the Result

If the calculated t-value is greater than the critical t-value at the chosen significance level, then the null hypothesis is rejected. That would suggest that the mean wrist extension is greater than 20 degrees with a 95% confidence.

Check Assumptions

Make sure the assumptions for the test are met - data follows a normal distribution or the sample size is large enough (and having no outliers). If these assumptions are not met, the results may not be reliable. To generalize these results to all Cornell students or all university students, the sample would need to be representative of the respective population.