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

A sample of 12 in-state graduate school programs at school A has a mean tuition of \(64,000 with a standard deviation of \)8,000. At school B, a sample of 16 in-state graduate programs has a mean of \(80,000 with a standard deviation of \)6,000. On average, are the mean tuitions different?

Short answer

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

Step-by-step solution

Given information

12 in-state graduate school programs of school A has $\$64000$ mean tuition and standard deviation of $\$8000.$

16 in-state graduate school program of school B has$\$80000$ mean and standard deviation of $\$6000.$

The most appropriate hypothesis test for the supplied data.

Assuming school A average tuition as ${\mu }_{\mathrm{A}}$

Assuming school B average tuition as ${\mu }_{\mathrm{B}}$

The null and alternative hypothesis is given as

$$\begin{gathered} {\mathrm{H}}_0:{\mu }_A={\mu }_B \\ {H}_a:{\mu }_A\ne {\mu }_B \end{gathered}$$

This demonstrates that this hypothesis test is for unknown variances, population standard deviations, and/or independent group means.