Question

Consider the following hypothesis test.

H₀: μ_d ≤ 0

H_a: μ_d > 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

s_d.

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 =

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