hypothesis test for a population mean A+ Writers | apluswriters.net

## 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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Here are the directions, grading rubric, and definition of *high-quality feedback* for the discussion board exercises.

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

### Prompt

- In a previous lab we tested the following hypotheses,

${}_{}$

H

0

:

$\mathrm{\xce\xbc}$

=

4.73

and

${}_{}$

H

a

:

$\mathrm{\xce\xbc}$

<

4.73

(where

$\mathrm{\xce\xbc}$

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.

**$\mathrm{\xce\xbc}$**

**:**Mean of variable**${}_{}$**

H

0

$\mathrm{\xce\xbc}$**:**

=

4.73

${}_{}$

H

A

:

$\mathrm{\xce\xbc}$

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.

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

- In a previous matched pairs lab we tested the following hypotheses, where

$\mathrm{\xce\xbc}$

is the mean of the differences in corn yield for a plot of land (

*regular seed minus kiln-dried*): H_{0}: Âµ = 0 and H_{a}: 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.

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

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