Question

The known standard deviation in salary for all mid-level professionals in the financial industry is $\backslash (11,000$. Company A and Company B 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.

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

Short answer

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

Step-by-step solution

Given information

In the finance industry, the standard deviation in salary of mid-level professionals is $\$11,000$. Samples are taken from company A and B which are in finance industry.

For company A, salary mean is $\$80,000$, while for Company B it is $\$96,000$.Management of both companies seek if they are paying their midlevel professionals differently.

Calculation

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

Samples are taken from company A and B which are in finance industry.

For company A, salary mean is $\$80000,$while for Company B it is $\$96000$.

Management of both companies seek if they are paying their midlevel professionals differently.

Assuming mean salary of mid-level professionals of Company A as ${\mu }_A$.

Assuming mean salary of mid-level professionals of Company B as ${\mu }_{\mathrm{B}}$.

The null and alternative hypothesis is given as :

$$\begin{gathered} {\mathrm{H}}_0:{\mu }_{\mathrm{A}}={\mu }_{\mathrm{B}} \\ {\mathrm{H}}_{\mathrm{a}}:{\mu }_{\mathrm{A}}\ne {\mu }_{\mathrm{B}} \end{gathered}$$

Hence, this shows that this hypothesis test is for independent group means, population standard deviations, and/or variances known.

Final answer

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