Question

Use the following information to answer the next $15$exercises: Indicate if the hypothesis test is for

a. independent group means, population standard deviations, and/or variances known

b. independent group means, population standard deviations, and/or variances unknown

c. matched or paired samples

d. single mean

e. two proportions

f. single proportion

The known standard deviation in salary for all mid-level professionals in the financial industry is $\backslash (11,000.$ Company A and CompanyB are in the financial industry. Suppose samples are taken of mid-level professionals from Company A and from Company B. The sample mean salary for mid-level professionals in Company A is$\backslash )80,000.$ The sample mean salary for mid-level professionals in Company B is $\$96,000.$ Company A and Company B management want to know if their midlevel professionals are paid differently, on average.

Short answer

The test is for known variances, population standard deviations, and independent group means.

Step-by-step solution

Given information

The standard deviation in the salary of mid-level professionals is $\$11,000$.

The salary mean of company A is role="math" localid="1650295431118" $\$80,000$.

The salary mean of company B is $\$96.000$.

Explanation

Assuming that the average compensation of Company A's mid-level professionals is ${\mu }_A$

Assuming that the average wage of Company B's mid-level professionals is${\mu }_B$

The null and alternative hypothesis is given as

$$\begin{gathered} H_0:{\mu }_A={\mu }_B \\ {H}_a:{\mu }_A\ne {\mu }_B \end{gathered}$$

This demonstrates that the hypothesis test is for independent group means with known population standard deviations and variances.