# Test for A Difference in Two Population Means

Question Description
Learn by Doing
In this activity you will learn to use StatCrunch to perform a two-sample t-test.

Some features of this activity may not work well on a cell phone or tablet. We highly recommend that you complete this activity on a computer.

Here are the directions and grading rubric for the Learn by Doing discussion board exercises.

A list of StatCrunch directions is provided at the bottom of this page.

Context

A student conducted a study of sleep habits at a large state university. His hypothesis is that undergraduates will party more and sleep less than graduate students. He surveyed random samples of 75 undergraduate students and 50 graduate students. Subjects reported the hours they sleep in a typical night.

For this hypothesis test, he defined the population means as follows:

LaTeX: \mu_1 ? 1 is the mean number of hours undergraduate students sleep in a typical night.
LaTeX: \mu_2 ? 2 is the mean number of hours graduate students sleep in a typical night.
Variables
Hours: typical number of hours a student sleeps each night

Program is the explanatory variable, and the data is categorical. Hours is the response variable, and the data is quantitative.

Data
Two sample T hypothesis test:
?1 – ?2 : Difference between two means
H0 : ?1 – ?2 = 0
HA : ?1 – ?2 < 0
(without pooled variances)

Hypothesis test results:
DifferenceSample Diff.Std. Err.DFT-StatP-value ?1 – ?2-0.233333330.18963708106.32776-1.23042040.1106

Prompt
State the null and alternative hypotheses. Include a clear description of the populations and the variable.
Explain why we can safely use the two-sample T-test in this case.
Use StatCrunch to carry out the test.
Copy and paste the content of in the StatCrunch output window (text and the table) in your initial post.
State a conclusion in the context of this problem.