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	19
2	28	27
3	18	17
4	20	17
5	26	23

(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?

Reject H₀. There is sufficient evidence to conclude that

μ_d > 0.

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.

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	Di
21	19	2
28	27	1
18	17	1
20	17	3
26	23	3

From given data, we have

Part b

Dbar = 2

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 = (2 - 0)/[1/sqrt(5)]

t = 4.4721

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

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