Question

You wish to test the following claim (H) at a significance level of a 0.10 H.: -724 H.72.4 You believe the population is normally distributed, but you do not know the standard deviation data 30.9 27 58.4 a. What is the test statistic for this sample? test statistic Round to 3 1 to 3 decimal places b. What is the p-value for this sample? p-value Round to 4 decimal places c. The p-value is.. Oless than (or equal to) a greater than a d. This test statistic leads to a decision to... reject the null Oaccept the null fail to reject the null c. As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 72.4. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 72.4. The sample data support the claim that the population mean is not equal to 72.4 There is not sufficient sample evidence to support the claim that the population mean is not equal to 724 Box 1: Enter your answer as an integer or decimal number. Examples: 3.-4.5.3172 Enter DNE for Does Not Exist, co for Infinity

Answer 1

Solution: The provided sample mean is I = 41.18 and the sample standard deviation is s = 14.78, and the sample size is n = 4. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Họ: A = 72.4 Hau 672.4 This corresponds to a two-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 = 0.10, and the critical value for a two-tailed test is te = 2.353. The rejection region for this two-tailed test is R = {t : It > 2.353} (3) Test Statistics The t-statistic is computed as follows: 41.18 - 72.4 4.225 14.78/74 I - o t= (4) Decision about the null hypothesis Since it is observed that t) = 4.225 > t = 2.353, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0.0243, and since p = 0.0243< 0.10, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean u is different than 72.4, at the 0.10 significance level.