Question

Consider a test of

H0 : μ = μ0 vs. H0 : μ < μ0.

Suppose this test is based on a sample of size 8, that σ2 is known, and that the underlying population is normal. If a 5% significance level is desired, what would be the rejection rule for this test?

Answer 1

This is a one sample test for mean

Though is known , as sample size is small , we use t test for mean

Test statistic is given by

For rejection rule we need to find critical value, tc

The test is left tailed as the alternative hypothesis is , rejection region would be in the left tail

degrees of freedom = n-1 = 8-1= 7

For 5% leve of significance ,with df =7 , critical value of t is

tc = - 1.89 (from t critical value table)

Thus rejection rule is

If calculated value of t < -1.89 , we reject the null hypothesis