A random sample of size n 10 is taken from a large populati

A random sample of size n = 10 is taken from a large population. Let be the population mean. It is desired to test: H0 :=12 vs. HA :=12, using = 0.1. A QQ plot indicates that normality can be assumed. From the sample, x = 14.2 and s = 4.88. (a) Since the data is normal and the population variance 2 is unkonwn, a t-test is appropriate here. Compute the p-value of the test. Would you reject or not reject? (b) Assume now that = 5 and HA : > 12. Compute the power of the test if the true population mean is A = 15. (c) Using = 5 and HA : > 12, what sample size would be required to achieve a power of 0.8 if the true population mean is A = 15? Give your answer as the smallest whole number that meets the criterion.

Solution