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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 15workers, and their average time with the company is five years with a standard deviation of 1.2.Company B samples 20workers, and their average time with the company is 4.5yearswith 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

01

Given information

A study is done to determine if Company A retains its workers longer than Company B. Company A samples 15workers, and their average time with the company is five years with a standard deviation of 1.2.Company B samples 20workers, and their average time with the company is 4.5years.with a standard deviation of0.8.The populations are normally distributed.1

02

Explanation (part a)

The population standard deviations are unknown.

03

Explanation (part b)

The null and alternative hypothesis is

H0:渭A=渭bHa:渭A>渭b

The significant level,

a=5%a=0.05

The p-value is which is much higher than 0.05so we decline to reject the null hypothesis.

Hence, there is no sufficient evidence to conclude that the workers of Company A stay longer with the company.

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