Suppose that you are testing the hypothesis H0 ∶

???? = 50 against the usual two-sided alternative. The data are normally distributed with known standard deviation ???? = 1.

The sample average obtained in the experiment is 50.5, and it is known that if the true population mean is actually 50.5, then this has no practical significance on the problem that motivated the experiment. Find the P-value for the t-test for the following sample sizes:

(a) n = 5

(b) n = 10

(c) n = 25

(d) n = 50

(e) n = 100

(f) n = 1000 Discuss your findings. What does this tell you about relying on P-values in hypothesis testing situations when sample sizes are large?