Question

Let the test statistic Z have a standard normal distribution when H₀ is true. Give the significance level for each of the following situations. (Round your answers to four decimal places.)

(a)    H_a: ? > ?₀, rejection region

z ? 1.77

(b)    H_a: ? < ?₀, rejection region

z ? ?2.62

(c)    H_a: ? ? ?₀, rejection region

z ? 2.81 or z ? ?2.81

Answer 1

We refer to the Z tables for this. Please don't hesitate to give a "thumbs up" for the answer in case you are satisfied with it.

(a)    Ha: ? > ?0, rejection region

z ? 1.77

The cumulative area for Z of 1.77 is .9606

Therefore, the significance level is 1-.9606 = .0394

(b)    Ha: ? < ?0, rejection region

z ? ?2.62

The rejection region is <=.0044

The significance level is .0044

(c)    Ha: ? ? ?0, rejection region

z ? 2.81 or z ? ?2.81

For this again, refer to the Z tables, .0025 and .9975, which means that we have rejection region as <.0025 or >.9975 . Hence, signifcance level is .0025