Module 22 – Hypothesis Test for a Population Mean (17 of 19 discussion 3) AND Unit 8 Checkpoint: Inference for Means

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

Prompt

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

   
   0
   :

   $\mu$
   

   
   =
   
   
   4.73
   and

   $H$
   

   
   a
   :

   $\mu$
   

   
   <
   
   
   4.73
   (where

   $\mu$
   

   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.
   

   $\mathrm{<br>\; \mu <br>}$
   

   : Mean of variable
   

   ${}_{}$
   
   H
   
   
   

   
   0
   :

   $\mu$
   

   
   =
   
   
   4.73
   
   

   $H$
   

   
   A
   :

   $\mu$
   

   
   ≠
   
   
   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
   $\mu$
   

   is the mean of the differences in corn yield for a plot of land (regular seed minus kiln-dried): H0: µ = 0 and Ha: µ < 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:
   

   $\mu$
   

   
   D
   
   
   =
   
   
   
   μ
   
   
   1
   
   
   
   −
   
   
   
   μ
   
   
   2
   
   : Mean of the difference between Regular seed and Kiln-dried seed
   

   $H$
   

   
   0
   :

   $\mu$
   

   
   D
   
   
   =
   
   
   0
   
   

   $H$
   

   
   A
   :

   $\mu$
   

   
   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.

Unit 8 Checkpoint: Inference for Means( Exam or Quiz)

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