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	25
3	18	16
4	20	19
5	26	25

(b)

Compute

d.

(c)

Compute the standard deviation

s_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?

Answer 1

a)

                         Population

Element           1                   2                         Difference

1                     21               18                              3

2                     28               25                              3

3                     18               16                              2

4               20 19    1      

5                     26               25                              1

b) = (3 + 3 + 2 + 1 + 1)/5 = 2

c) s_d = sqrt(((3 - 2)^2 + (3 - 2)^2 + (2 - 2)^2 + (1 - 2)^2 + (1 - 2)^2)/4) = 1

The test statistic is

  

P-value = P(T > 4.472)

             = 1 - P(T < 4.472)

            = 1 - 0.9945

            = 0.0055

Since the P-value is less than , so we should reject the null hypothesis.