Question

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

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?

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.

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