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	21
2	28	28
3	18	17
4	20	18
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 =

What is your conclusion?

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

μ_d > 0.

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

μ_d > 0.

     Reject H₀. There is insufficient evidence to conclude that

μ_d > 0.

Reject H₀. There is sufficient evidence to conclude that

μ_d > 0.

Answer 1

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.

Part a

Pop1	Pop2	Difference
21	21	0
28	28	0
18	17	1
20	18	2
26	24	2

From given data, we have

Part b

Dbar = 1

Part c

Sd = 1

n = 5

df = n – 1 = 4

α = 0.05

Part d

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (1 - 0)/[1/sqrt(5)]

t = 2.2361

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

P-value = 0.0445

P-value < α =0.05

So, we reject the null hypothesis

Reject H0. There is sufficient evidence to conclude that μd > 0.