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 18
2 28 27
3 18 15
4 20 19
5 26 24

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 =

Homework Answers

Answer #1

Solution:

Part A

The table for differences is given as below:

Population 1

Population 2

Difference Di

21

18

3

28

27

1

18

15

3

20

19

1

26

24

2

Part B

d̄ = ∑Di/n = 10/5 = 2

Part C

Sd = 1.0000

[By using excel]

Part D

Here, we have to use paired t test.

The null and alternative hypotheses for this test are given as below:

H0: µd = 0 versus Ha: µd > 0

This is a right tailed test.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

Dbar = 2

Sd = 1

n = 5

df = n – 1 = 4

α = 0.05

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (2 – 0)/[1/sqrt(5)]

t = 4.472

Test statistic = 4.472

The p-value by using t-table is given as below:

P-value = 0.0055

P-value < α = 0.05

So, we reject the null hypothesis

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