Question

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 $4.5\text{years}$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

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 $4.5\text{years.}$with a standard deviation of$0.8.$The populations are normally distributed.$1$

Explanation (part a)

The population standard deviations are unknown.

Explanation (part b)

The null and alternative hypothesis is

$$\begin{gathered} H_0:{\mu }_{\mathrm{A}}={\mu }_b \\ {H}_a:{\mu }_{\mathrm{A}}>{\mu }_b \end{gathered}$$

The significant level,

$$\begin{gathered} a=5\% \\ a=0.05 \end{gathered}$$

The p-value is which is much higher than $0.05$so 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.