Reconsider the data from Medicine and Science in Sports and Exercise described in Exercise 8-32. The sample size was seven and the sample mean and sample standard devi ation were 315 watts and 16 watts, respectively. (a) Is there evidence that leg strength exceeds 300 watts at significance level 0.05? Find the P-value.

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19-12-2022
Mathematics

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Reconsider the data from Medicine and Science in Sports and Exercise described in Exercise 8-32. The sample size was seven and the sample mean and sample standard devi ation were 315 watts and 16 watts, respectively. (a) Is there evidence that leg strength exceeds 300 watts at significance level 0.05? Find the P-value.

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varshamittal029 varshamittal029 · Answer 1 · 2022-12-22T04:53:04-05:00

Using the t-distribution, it is found that the 95% confidence interval for the mean peak power after training is (301.2, 328.8).

We have the standard deviation for the sample, thus, the t-distribution is used.

The sample mean is 315.

The sample standard deviation is s = 16.

The sample size is n = 7.

The interval is:

mean ± t s/√n

To build the interval, we need to find the critical value, which looking at the t-table for a 95% confidence interval with 8 - 1 = 7 df is t = 2.4469.

Then, replacing the values:

315 - 2.4469 16/√8 = 301.2

315 + 2.4469 16/√8 = 328.8

The 95% confidence interval for the mean peak power after training is (301.2, 328.8).

Learn more about Confidence Interval here:

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