Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 25 - Hypothesis Test with Technology (discussion 1)

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2026-01-17T21:14:50-08:00

1. Since we want to check whether the data supports the claim that undergraduate students sleep less, on average, than graduate students, we are testing:
:

:

2. We can safely use the two-sample T-test in this case since:

Both samples are random, and therefore independent.

The sample sizes (75 and 50) are quite large, and therefore we can proceed regardless of whether the populations are normal or not.

3. T = -1.23; P-value = 0.111

Here is the StatCrunch output depicting these values.

Two sample T hypothesis test:
: Mean of undergraduate
: Mean of graduate
:
:
(without pooled variances)

Hypothesis test results:

Difference | Sample Diff. | Sd. Err. | DF | T-Stat | P-Value
μ₁ - μ₂ | -0.23333333 | 0.18963708 | 106.32776 | -1.2304204 | 0.1106

4. The P-value (0.111) is greater than 0.05. This indicates that the observed data is not unusual if undergraduate and graduate students, on average, have the same mean for sleep hours. Therefore, the data do not provide evidence to reject . So we cannot conclude that undergraduate students sleep less, on average, than graduate students.