The Santa Rosa Swim Club dominates American swimming, having produced more elite swimmers than any other swim club in the country. The swim club recently participated in a study evaluating the merits of two new breathing techniques for competitive swimmers. In the study, a sample of 120 swimmers was asked to use Technique A in their swim training for two months. A similar sample of 120 swimmers was asked to use Technique B. Swimmers in both samples were tested before and after the trial months and efficiency increases were measured. In the Technique A sample, 60 swimmers showed “substantial improvement” in breathing efficiency. In the Technique B sample, 54 swimmers showed a similar level of improvement. 

a. Use the normal sampling distribution of the sample proportion difference to test the null hypothesis that the proportion of swimmers who would experience “ substantial improvement“ in breathing efficiency is the same for the two populations of swimmers represented by the samples. (You may want to review the Chapter 10 discussion of tests for proportion differences.) Use a significance level of .05.

b. Now perform the same test, but this time use the chi square distribution and an appropriate table format. Compare your results to your results in part a.