Question

A random sample of size 27 from a normal distribution has standard deviation s= 56. Test H0:= 58 versus H1: not equal 58. It's a two tailed test. Use the a= 0.10 level of significance. Find the critical values

Answer 1

To find the critical values for a two-tailed test with a significance level of 0.10, we first need to find the critical z-scores.

Since the alternative hypothesis is not equal to 58, it is a two-tailed test. Our significance level is 0.10, which means 0.05 on each tail. We need to find the critical z-scores that correspond to a cumulative probability of 0.05 in the lower tail and 0.95 in the upper tail.

Using a standard normal distribution table or a calculator, we find that the critical z-scores are approximately -1.645 and 1.645.

Therefore, the critical values for this two-tailed test at a 0.10 level of significance are -1.645 and 1.645.