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	27
3	18	16
4	20	18
5	26	26

(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

a)

H₀: μ_d ≤ 0

H_a: μ_d > 0

	population
1	2	diff(d)=1-2	(d-dbar)^2
21	21	0	1
28	27	1	0
18	16	2	1
20	18	2	1
26	26	0	1
	sum	5	4
	Mean(d)=dbar=sum(d)/n	1
	standard deviation(sd)=sqrt(sum(d-dbar)^2/n-1)	1

b) dbar=sum(d)/n=5/5=1

c)

standard deviation(sd)

sd=sqrt(sum(d-dbar)^2/n-1)=4/(5-1)=1