Question

Consider the following hypothesis test. H0: μd ≤ 0 Ha: μd > 0 (a) The following...

Consider the following hypothesis test.

H0: μd ≤ 0

Ha: μd > 0

(a)

The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 − Population 2.)

Element Population Difference
1 2
1 21 20
2 28 27
3 18 16
4 20 17
5 26 23

(b)

Compute

d.

(c)

Compute the standard deviation

sd.

(d)

Conduct a hypothesis test using

α = 0.05.

Calculate the test statistic. (Round your answer to three decimal places.)

Calculate the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Do not Reject H0. There is sufficient evidence to conclude that

μd > 0.

Reject H0. There is sufficient evidence to conclude that

μd > 0.

    Reject H0. There is insufficient evidence to conclude that

μd > 0.

Do not reject H0. There is insufficient evidence to conclude that

μd > 0.

Homework Answers

Answer #1

H0: μd ≤ 0

Ha: μd > 0

test statistics:

before   after   dbar
21   20   1
28   27   1
18   16   2
20   17   3
26   23   3


dbar = μ(before) - μ(after) = 2
s(dbar) = 1

SE = s(dbar)/sqrt(n)  
= 1/sqrt(5)
= 0.4472

Test Statisitcs,
t = dbar/SE  
= 2/0.4472
= 4.4721


p value = 0.0055
As p value < 0.05

Reject H0. There is sufficient evidence to conclude that

μd > 0.


.

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