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Suppose you want to test the claim the the paired sample data given below come from...

Suppose you want to test the claim the the paired sample data given below come from a population for which the mean difference is μd=0. xy7866678183687180529154928286 Use a 0.01 significance level to find the following: (a) The mean value of the differnces d for the paired sample data d¯= (b) The standard deviation of the differences d for the paired sample data sd= (c) The t test statistic t= (d) The positive critical value t= (e) The negative critical value t= (f) Does the test statistic fall in the critical region? A. No B. Yes (g) Construct a 99% conficence interval for the population mean of all differences x−y. <μd

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Answer #1

Computational Table:

X Y d=x-y d^2
78 66 12 144
67 81 -14 196
83 68 15 225
71 80 -9 81
52 91 -39 1521
54 92 -38 1444
82 86 -4 16
Total -77 3627

a)

b)

c) Test statistic:

d)

Degrees of freedom = n-1 = 7-1 = 6

Critical value:

...............................From t table

Therefore,

Positive Critical value: 3.7074

Negative Critical value: -3.7074

Conclusion:

Test statistic (t) lies in the rejection region,i.e. -3.7074 < -1.35 < 3.7074, That is Fail to Reject Ho at 1% level of significance.   

f) Yes, Test statistic -1.35 is Falls in the critical region

g) Construct 99% Confidence interval:

We are 99% Confidence that population mean difference is lies in that interval.

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