Question

You wish to test the following claim ( H a ) at a significance level of α = 0.002 . H o : μ = 67.5 H a : μ > 67.5 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 34 with mean M = 69.2 and a standard deviation of S D = 19.7 . What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =

Answer 1

The provided sample mean is X = 69.2 and the sample standard deviation is s = 19.7, and the sample size is n = 34. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: u = 67.5 Ha: u > 67.5 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 = 0.002, and the critical value for a right-tailed test is te = 3.094. The rejection region for this right-tailed testis R=t:t>3.094 (3) Test Statistics The t-statistic is computed as follows: X - μo ta 69.2 - 67.5 19.7/34 0.503 s/Vn (4) Decision about the null hypothesis Since it is observed that t = 0.503 <tc = 3.094, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p=0.3091, and since p= 0.3091 > 0.002, 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 67.5, at the 0.002 significance level.

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