A matched pairs experiment is carried out, yielding the following data: nD=57, x

Question

A matched pairs experiment is carried out, yielding the following data:

nD=57, x¯D=1.6, sD=5.3

Is there evidence, at an =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 (,a) is expressed (-infty, a), an answer of the form (b,) is expressed (b, infty), and an answer of the form (,a)(b,) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Reject H0. B. Reject H1. C. Do Not Reject H0. D. Do Not Reject H1.

Explanation / Answer

Null hypo: H0: mu(D) = 0
Alternate hypo: Ha: mu(D) not equals to 0

A)
Test statistics
t = (1.6 - 0)/(5.3/sqrt(57))
t = 2.2792

B)
df = 56
Rejection region is (-infty, -1.8472) U (1.8472, infty)

C)
p-value = 0.0265

D)
Reject the null hypothesis as p-value is less than 0.07

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