The following are matched data fromtwo populations: Element Population1 Populati

Question

The following are matched data fromtwo populations:

Element          Population1               Population 2

1                     31                               30

2                     31                               30

3                     30                               30

4                     33                               30

5                     32                               29

(Round your answers to two decimal places. Example:1.51)

For the hypothesis test:

a. What is the sample mean for thedifference values?

b. What is the samplestandard deviation for the difference values?

c. What is the teststatistic?

Explanation / Answer

Element ---- Difference 1 ----------- 1 2 ----------- 1 3 ----------- 0 4 ----------- 3 5 ----------- 3 Mean = (1 + 1 + 0 + 3 + 3)/5 = 1.6 sample standard deviation = [(1-1.6)2 +(1-1.6)2 + (0-1.6)2 + (3-1.6)2 +(3-1.6)2]/4 = 1.3416 t = 1.6/[1.3416/5]= 2.67 With 4 degrees of freedom, this gives a p-value of 0.028 Reject the null hypothesis at the =.05 level

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