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.

Answer

p-value = 0.007

Write down the null hypothesis and the alternative hypothesis. Null Hypothesis = H0: μ ≤ 300, Alternative Hypothesis = H1: μ > 300.
Determine the test statistic. t = (x̄ - μ) / (s / √n), where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Calculate the value of the test statistic. t = (315 - 300) / (16 / √7) = 4.11.
Find the p-value. Using a t-distribution table with 6 degrees of freedom (7-1), the area to the right of 4.11 is approximately 0.007. Therefore, the p-value is 0.007.