Question

appos is an online retailer based in Nevada and employs 1,300 employees. One of their competitors, Amazon.com, would like to test the hypothesis that the average age of a Zappos employee is less than 36 years old. A random sample of 22 Zappos employees was found to have an average age of 33.9 years. The standard deviation for this sample was 4.1 years. Amazon would like to set α = 0.025. The conclusion for this hypothesis test would be that because the test statistic is

1. more than the critical value, we can conclude that the average age of Zappos employees is less than 36 years old.

2. more than the critical value, we cannot conclude that the average age of Zappos employees is less than 36 years old.

3. less than the critical value, we can conclude that the average age of Zappos employees is less than 36 years old.

4. less than the critical value, we cannot conclude that the average age of Zappos employees is less than 36 years old

Answer 1

As we are testing here whether the average age of a Zappos employee is less than 36 years old, therefore this is a lower tailed test specifically a lower tailed test. For 0.025 level of significance, and n - 1 = 21 degrees of freedom, we have from t distribution tables:
P( t₂₁ < -2.080) = 0.025

Therefore -2.080 is the critical value here.

The test statistic here is computed as:

As the test statistic here is -2.40 < -2.08 which is the critical value, therefore it lies in the rejection region and we can reject the null hypothesis here.

Therefore as the test statistic is less than the critical value, we can conclude that the average age is less than 36 years old.