Zappos 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 ? = 0.025. The test statistic for this hypothesis test would be .

Question

Quizplus · Accepted Answer

The test statistic for this hypothesis test is calculated using the formula for a t-test because the population standard deviation is unknown and the sample size is less than 30. The formula for the t-test statistic is $$t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values ($\bar{x} = 33.9$, $s = 4.1$, $n = 22$, and testing against $\mu = 36$), we find that the calculated t-statistic is closest to the value given in option A, -2.40. This indicates that the average age of a Zappos employee is statistically significantly less than 36 years old at the $\alpha = 0.025$ level, assuming the calculation for -2.40 is correct based on the provided information.

Zappos Is an Online Retailer Based in Nevada and Employs txˉt \bar { x }txˉ

Zappos Is an Online Retailer Based in Nevada and Employs $t \bar { x }$