Reference no: EM132474342

A random sample of size n = 10 is taken from a large population. Let µ be the unknown population mean. A test is planned of H0 : µ = 12 vs. HA : µ ≠ 12 using α = 0.1. A QQ plot indicates it is reasonable to assume a normal population. From the sample, x¯ = 14.2 and s = 4.88. (I suggest doing this problem with a calculator and/or table as practice for exams. You may check your answers with R if you wish.)

(a) Since the data leave it plausible that the population is normal, and the population standard deviation σ is unknown, a t-test is appropriate. Compute the p-value of the test. Do you reject or not reject H0?

(b) Based on the test (and without calculating the interval), say whether you expect a 90% con?dence interval to include 12.

(c) Using s = 4.88 as our best guess of σ (that is, pretending we know σ = 4.88), compute the power of a future test of H0 : µ = 12 vs. HA : µ ≠ 12 if the true population mean is µA = 15.

(d) Using s = 4.88 as our best guess of σ (that is, pretending we know σ = 4.88), approximately what sample size would be required to achieve a power of 0.8 if the true population mean is µA = 15? Give your answer as the smallest whole number that meets the criterion.