Suppose that X1 Xn form a random sample from the normal dis

Suppose that X1 .... Xn form a random sample from the normal distribution with unknown mean mu and known variance 1. Suppose also that mu 0 is a certain specified number, and that the following hypothesis is to be tested H0 : mu = mu 0 vs HA : mu not equal to mu 0. Finally, suppose that the sample size n is 25, and consider a test procedure such that H0 is to be rejected if |X n - mu 0| geq c. Determine the value of c such that the size of the test will be 0.05.

Solution

Using a table, for a two tailed test at 0.05 significance,

|zcrit| = 1.96

As we see, we get c as

zcrit = (Xn - uo) / sigma

as sigma = 1, zcrit = 1.96, then

1.96 = |Xn - uo|(crit) / 1

Thus,

|Xn - uo|(crit) = 1.96 = c

Thus,

c = 1.96 [ANSWER]