Does the Speedo Fastskin II Male Hi-Neck Bodyskin competition racing swimsuit improve a swimmer's 200-yard individual medley performance times? A test of 100 randomly chosen male varsity swimmers at several different universities showed that 66 enjoyed improved times,compared with only 54 of 100 female varsity swimmers.To test for equality in the proportions of men versus women who experienced improvement,the test statistic is approximately

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We can use a two-sample proportion z-test to test for equality in the proportions of male and female swimmers who experienced improvement in their 200-yard individual medley performance times. The test statistic is calculated as follows:
z = (p₁ - p₂) / sqrt(p̂(1 - p̂) * (1/n₁ + 1/n₂))
where p₁ and p₂ are the sample proportions of swimmers who experienced improvement, p̂ is the pooled proportion, n₁ and n₂ are the sample sizes.
Using the given data, we have:
p̂ = (66 + 54) / (100 + 100) = 0.60
z = (0.66 - 0.54) / sqrt(0.60 * 0.40 * (1/100 + 1/100)) = 1.73
The critical value for a two-tailed test at α = 0.05 is 1.96. Since the calculated test statistic (1.73) is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in the proportion of male versus female swimmers who experienced improvement in their 200-yard individual medley performance times.

Does the Speedo Fastskin II Male Hi-Neck Bodyskin Competition Racing