Question

It is thought that teenagers sleep more than adults on average. A study is done to verify this. A sample of 16 teenagers has a mean of 8.9 hours slept and a standard deviation of 1.2. A sample of 12 adults has a mean of 6.9 hours slept and a standard deviation of 0.6.

Short answer

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

Step-by-step solution

Given information

Teenagers are thought to sleep more than adults on average. The average number of hours worked by 16 teenagers was 8.9, with a standard deviation of 1.2.

The mean for a group of 12 adults is 6.9 hours, with a standard deviation of 0.6.

The most appropriate hypothesis test for the supplied data.

Assuming average hours of sleep for teenagers as ${\mu }_T$

Assuming an average of eight hours of sleep${\mu }_{\mathrm{A}}$

The alternative and null hypothesis are as follows:

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

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