Chapter 10: Q. 10.2 (page 572)

A study is done to determine if Company A retains its workers longer than Company B. Company A samples $15$ workers, and their average time with the company is five years with a standard deviation of $1.2 .$ Company B samples $20$ workers, and their average time with the company is $4.5 years$ with a standard deviation of $0.8 .$ The populations are normally distributed.
a. Are the population standard deviations known?
b. Conduct an appropriate hypothesis test. At the $5 %$ significance level, what is your conclusion?

Short Answer

Expert verified

a. The population standard deviations are unknown.

b. There is no sufficient evidence to conclude that the workers of Company A stay longer with the company.

Step by step solution

Given information

A study is done to determine if Company A retains its workers longer than Company B. Company A samples $15$ workers, and their average time with the company is five years with a standard deviation of $1.2 .$ Company B samples $20$ workers, and their average time with the company is $4.5 years.$ with a standard deviation of $0.8 .$ The populations are normally distributed. $1$