Use the Following Information to Answer the Question Assume That All Conditions for Testing Have Been Met

question 32

Multiple Choice

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed
by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours.
-A researcher wants to know whether athletic women are more flexible than non-athletic women. For this experiment, a woman who exercised vigorously at least four times per week was
Considered "athletic." Flexibility is measured in inches on a sit & reach box. Test the researcher's
Claim using the following summary statistics: $$\begin{array} { | l | l | } \hline \text { Athletic women } & \text { Non-athletic women } \\\hline n = 50 & n = 30 \\\hline \bar { x } = 5.0 \text { inches } & \bar { x } = 4.6 \text { inches } \\\hline s = 1.4 \text { inches } & s = 0.8 \text { inches } \\\hline\end{array}$$ Assume that all conditions for testing have been met. Report the test statistic and p-value. At the
1% significance level, state your decision regarding the null hypothesis and your conclusion about
The original claim. Round all values to the nearest thousandth.

• A) \(t = - 1.623 ; p = 0.054\); Reject the null hypothesis; there is strong evidence to suggest that athletic women are more flexible than non-athletic women.
• B) \(t = - 1.623 ; p = 0.108\); Reject the null hypothesis; there is strong evidence to suggest that athletic women are more flexible than non-athletic women.
• C) \(t = 1.623 ; p = 0.108\); Reject the null hypothesis; there is not strong evidence to suggest that athletic women are more flexible than non-athletic women.
• D) \(t = 1.623 ; p = 0.054\); Fail to reject the null hypothesis; there is not strong evidence to suggest that athletic women are more flexible than non-athletic women.

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