Question 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?
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?
{:[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