Question

The average mile time for girls high school track is 5:17, with a standard deviation of 6.9 seconds. Coach Dart believes that he has perfected his training methods to a degree that his female milers can consistently run faster than your average girl’s high school miler. The average mile time for the 8 girls on his team who run that distance is 5:12. Calculate the required statistic to determine if Coach Dart is correct, that his girls are significantly different from the total population of high school milers in girls track. Assume you are conducting a two-tailed test with a .05 level of significance. Don't forget to convert the times to seconds before doing your calculations.

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Answer 1

The provided sample mean is X = 312 and the known population standard deviation is o = 369, and the sample size is n = 8. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:u= 317 Ha: u 7 317 This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a two-tailed test is ze = 1.96. The rejection region for this two-tailed test is R= {z: 2] > 1.96} (3) Test Statistics The z-statistic is computed as follows: X - MO 312 - 317 369/18 -0.038 on (4) Decision about the null hypothesis Since it is observed that 2 = 0.038 < ze = 1.96, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.9694, and since p = 0.9694 > 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean u is different than 317, at the 0.05 significance level. Confidence Interval The 95% confidence interval is 56.301 <u < 567.699.

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