Question

The accompanying table shows two samples that were collected as matched pairs. Complete parts (a) through (d) below.

Pair:

1 7 5

2 5 2

3 8 7

4 4 5

5 5 1

6 9 9

a. State the null and alternative hypotheses to test if the populatio represented by Sample 1 has a higher mean than the population represented by Sample 2. Let ud be the population mean of matched-pair differences for Sample 1 minus Sample 2. Choose the correct answer below.

b. Calculate the appropriate test statistic and interpret the results of the hypothesis test using a=0.05.

c. Identify the p-value and interpret the result.

d. What assumptions need to be made in order to perform this procedure?

Answer 1

a)

H0 : mud = 0
HA: mud not=0

b)

Before    after   dbar
7   5   2
5   2   3
8   7   1
4   5   -1
5   1   4
9   9   0

dbar = μ(before) - μ(after) = 1.5
s(dbar) = 1.8708

SE = s(dbar)/sqrt(n)
= 1.8708/sqrt(6)
= 0.7638

Test Statisitcs,
t = dbar/SE  
= 1.5/0.7638
= 1.9640

c)

p value= 0.1067

Fail to reject H0 as p value > 0.05 significance level

d)

The sample of paired differences must be reasonably random.

The paired differences d = x1 - x2 should be approximately normally distributed or be a large
sample (need to check n ≥ 30 ). This procedure is robust if there are no outliers and little skewness in the paired differences.