To compare the performance of two swimmers, their 100m freestyle times were recorded independently of one another at random 10 times during both practice and competition. Swimmer 1 Swimmer 2 59.62 59.81 59.74 59.41 59.48 59.32 59.43 59.63 59.65 59.76 59.72 59.50 59.50 59.64 59.63 59.83 60.01 59.86 59.68 59.51 a. Compute a 95% confidence interval for the difference in the average times for Swimmer 1 and Swimmer 2. b. Perform a hypothesis test of the difference between the two swimmers average 100m freestyle times. Is there evidence that Swimmer 2 is on average faster than Swimmer 1? Assume a Type I error rate of ? = 0.05.
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Swimmer 1: Mean = 59.585, Standard Deviation = 0.165 Swimmer 2: Mean = 59.688, Standard Deviation = 0.155 Show more…
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David N.
Medley In the $4 \times 100$ medley relay event, four swimmers swim 100 yards, each using a different stroke. A college team preparing for the conference championship looks at the times their swimmers have posted and creates a model based on the following assumptions: $\bullet$ The swimmers' performances are independent. $\bullet$Each swimmer's times follow a Normal model. $\bullet$The means and standard deviations of the times (in seconds) are as shown: $$\begin{array}{|c|c|c|c|c|}\hline{\text { Swimmer }} & {\text { Mean }} & {\text { SD}} \\ \hline{1 \text { (backstroke) }} & {50.72} & {0.24}\\\hline {2 \text { (breaststroke) }} & {55.51 } & {0.22}\\\hline {3 \text { (butterfly) }} & {49.43 } & {0.25}\\\hline {4 \text { (freestyle) }} & {44.91 } & {0.21}\\ \hline \end{array}$$ a) What are the mean and standard deviation for the relay team’s total time in this event? b) The team’s best time so far this season was 3:19.48. (That’s 199.48 seconds.) Do you think the team is likely to swim faster than this at the conference championship? Explain.
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In a relay event, four swimmers swim 100 yards, each using a different stroke. A college team looks at the times for the swimmers and creates a model based on the assumptions that the swimmers' performances are independent, each swimmer's times follow a normal model, and the means and standard deviations of the times in seconds are as shown in the table. a) What are the mean and the standard deviation for the relay team's total time in this event? (Round to two decimal places as needed.)
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