A sample of 64 observations is selected from a normal popula

A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level. (a) Is this a one- or two-tailed test? (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding H0? (e) What is the p-value? Interpret it.

Solution

1. It is a One- tailed test. (H1 tells you that).

2. The decision rule is as follows.

invNorm (0.025) = -1.96

Reject Ho if z < -1.96

3. The value of test static is

z(215) = (215-220)/[15/sqrt(64)] = -2.6667

4. The p value is

p-value = p(z < -2.667) = normalcdf(-100,-2.667) = 0.0038