Question

In a test of the hypothesis Ho: u = 59 versus Ha: u>59, a sample of n = 100 observations possessed mean x = 58.5 and standard deviation s = 3.8. Find and interpret the p-value for this test. The p-value for this test is (Round to three decimal places as needed.)

Answer 1

The provided sample mean is X = 58.5 and the sample standard deviation is s = 3.8, and the sample size is n = 100. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: u = 59 Ha: u > 59 This corresponds to a right-tailed test, for which a t-test for one mean, with unknown 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 right-tailed test is te = 1.66. The rejection region for this right-tailed test is R=t:t>1.66 (3) Test Statistic The t-statistic is computed as follows: X - μo t= 58.5 - 59 3.8/100 = -1.316 s/n (4) Decision about the null hypothesis Since it is observed that t = -1.316 <te = 1.66, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.9044, and since p= 0.9044 > 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 greater than 59, at the 0.05 significance level.