The data for a random sample of 10 paired observations are shown
in the following

table

Pair Population 1 Population 2

1 19 24

2 25 27

3 31 36

4 52 53

5 49 55

6 34 34

7 59 66

8 47 51

9 17 20

10 51 55

(a) If you wish to test whether these data are sufficient to
indicate that the mean for

population 2 is larger than that for population 1, what are the
appropriate null

and alternative hypotheses? Define any symbols you use.

(b) Conduct the test from part (a), using α = .10. What is your
decision?

(c) Find a 90% confidence interval for μd. Interpret this
interval.

(d) What assumptions are necessary to ensure the validity of the
preceding analysis?

Community Answer

{:[s^(')d=-37],[id^(2)=181]:}The Sample numiber of soscrvation (n)=10 (# of d-values).The degrees of treedom (df)=n-1=9For paired observations.{:[M_(d)=(" population "1)-(" population "2)],[d=" difference "]:}pair 123456789mean of differencer bar(d)=(3^(2)d)/(n)=(-37)/(10)=-3.7Standard deviation of differencex S=sqrt((1)/((n-1))(Sigmad^(2)-((zd^(2))/(n))){:[S_(d)=sqrt((1)/(9)(181-((-37)^(2))/(10)))=sqrt9],[S_(d)=sqrt4.9=2.2136]:}(a) (i) Claim: The mean for population 2 is larger than that for population 1. i.e; mu_(d) < 0.H_(0):mu_(d)=0 versus H_(a):mu_(d) < 0.Type of test: Lett-tailed test. (one-tikedtest)(ii) The test statistic t=(d-mu_(d))/(((5d//sqrtn))/())=((-3.7-0))/(((2.2136)/(sqrt10))) t=(- ... See the full answer