Question

(1 point) A matched pairs experiment is carried out, yielding the following data: np = 75, ID = -1.2, p = 7.4 Is there evidence, at an a = 0.07 level of significance, to conclude that there is a difference between the two sets of measurements? Carry out an appropriate hypothesis test, filling in the information requested. A. The value of the standardized test statistic: Note: For the next part, your answer should use interval notation. An answer of the form (-0, a) is expressed (-infty, a), an answer of the form (b, ) is expressed (b, infty), and an answer of the form (-00, a) u (b, o) is expressed (-infty, a)(b, infty). B. The rejection region for the standardized test statistic: C. The p-value is

Answer 1

A) standardized test statistic t = X​​​​​​Dbar​​/( S​​​​​D/√nD)

t = -1.2/(7.4/√75)

​​​​​​t = -1.44

B) for level of significance a = 0.07 and d.f = n -1 = 74

tCritical = t​​​​​​a/2 , n-1 = t​​​​​​0.035, 74

tCritical = +/- 1.84

Rejection region is ( -infty , -1.84) U ( 1.84 , infty)

C) p-value for t = -1.44 and d.f = 74 , two tailed test

p-value = 2 * P( t < -1.44) d.f = 74

p-value = 0.1541