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 mu be the population mean. It is desired to test: H0 : mu = 12 vs. HA: 12, using a = 0.1. A QQ plot indicates that normality can be assumed. From the sample, x = 14.2 and s = 4.88. (I would suggest doing this problem with a hand calculator and statistical tables as practice for exam conditions, but you may check your answers using R if you wish.) (a) Since the data is normal and the population variance sigma ^2 is unknown, a ?-test is appropriate here. Compute the p-value of the test. Would you reject or not reject? Using sigma = 4.88 and a z-test, compute the power of the test if the true population mean is A = 15. Using sigma = 4.88 and a z-test, approximately what sample size would be required to achieve a power of 0.8 if the true population mean is mu = 15? Give your answer as the smallest whole number that meets the criterion.

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