Question

The data for a random sample of 8 paired observations are shown in the table to the right. a. What are the appropriate null and alternative hypotheses to test whether the mean for population 2 is larger than that for population​ 1? b. Conduct the test identified in part a using alphaαequals=0.100.10. c. Find a 9090​% confidence interval for mu Subscript dμd. Interpret this result. d. What assumptions are necessary to ensure the validity of this​ analysis? Pair Population 1 Population 2 1 2222 2727 2 5757 6363 3 4545 4747 4 2929 3333 5 5151 5757 6 3838 3838 7 3939 4242 8 3232 3737

Answer 1

Ans:

	population 1	population 2	d
1	22	27	5
2	57	63	6
3	45	47	2
4	29	33	4
5	51	57	6
6	38	38	0
7	39	42	3
8	32	37	5
		d-bar=	3.875
		sd=	2.100

b)

Test statistic:

t=(3.875-0)/(2.10/sqrt(8))

t=5.22

df=8-1=7

p-value=tdist(5.22,7,1)=0.0006

Reject the null hypothesis.

There is sufficient evidence to conclude that  the mean for population 2 is larger than that for population​ 1.

c)

critical t value=tinv(0.1,7)=1.895

90% confidence interval for mean difference

=3.875+/-1.895*(2.1/sqrt(8)

=3.875+/-1.407

=(2.468, 5.282)