# Module 22 – Hypothesis Test for a Population Mean (17 of 19 discussion 3) – Mod 22 Group 2

## Learn by Doing

This activity gives you practice explaining the different parts of the StatCrunch print-out for a hypothesis test for a population mean. You will review the meaning of standard error, T-scores and the P-value.

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### Prompt

1. In a previous lab we tested the following hypotheses, $H$

0
: $Î¼$

=

4.73
and $H$

a
: $Î¼$

<

4.73
(where $Î¼$

is the mean number of alcoholic drinks consumed by students at a liberal arts college).

In a random sample of 75 students, the mean was 3.93 alcoholic drinks consumed in a week. Here is the StatCrunch output from the hypothesis test. : Mean of variable ${}_{}$

H

0
: $Î¼$

=

4.73 $H$

A
: $Î¼$

â‰

4.73

Hypothesis test results
Variable Sample Mean Std. Err. DF T-Stat P-value
number of drinks per week 3.9333333 0.43592434 74 -1.8275343 0.0717

Using this context and the StatCrunch output, explain the meaning of each of the following.

1. Std. Err (standard error)
2. T-stat (T-score)
3. P-value
2. In a previous matched pairs lab we tested the following hypotheses, where $Î¼$

is the mean of the differences in corn yield for a plot of land (regular seed minus kiln-dried): H0: Âµ = 0 and Ha: Âµ < 0. In a random sample of 11 seeds of each type, the mean of the differences in the sample was -33.7. Here is a StatCrunch print-out of the hypothesis test.

Paired T hypothesis test: $Î¼$

D

=

Î¼

1

âˆ’

Î¼

2

: Mean of the difference between Regular seed and Kiln-dried seed $H$

0
: $Î¼$

D

=

0 $H$

A
: $Î¼$

D

<

0

Hypothesis test results
Difference Mean Std. Err. DF T-Stat P-value
Regular seed – Kiln-dried seed -33.727273 19.951346 10 -1.6904761 0.0609

Differences stored in column, Differences.

Using this context and the StatCrunch output, explain the meaning of each of the following.

1. Std. Err (standard error)
2. T-stat (T-score)
3. P-value.