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	20
2	28	27
3	18	16
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?

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

μ_d > 0.

Reject H₀. There is sufficient evidence to conclude that

μ_d > 0.

    Reject H₀. There is insufficient evidence to conclude that

μ_d > 0.

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

μ_d > 0.

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.

.