Question

A sample of 19 paired observations generates the following data: d = 1.2 and s2DsD2 = 2.4. Assume a normal distribution.

a. Construct the 95% confidence interval for the mean difference μ_D. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Confidence interval is_________to__________.

b. Using the confidence interval, test whether the mean difference differs from zero.

• There is evidence that the mean difference differs from zero.

• There is no evidence that the mean difference differs from zero.

Answer 1

solution:-

a. given that d = 1.2 , n = 19

and sd^2 = 2.4 then sd = 1.5492

degree of freedom df = n - 1 = 19 - 1 = 18

we look into t table with df = 18 and with 95% two tailed probability

critical value t = 2.101

confidence interval formula

=> d +/- t * sd/sqrt(n)

=> 1.2 +/- 2.101 * 1.5492/sqrt(19)

=> 0.45 to 1.95

b. Using the confidence interval, test whether the mean difference differs from zero.

=> There is no evidence that the mean difference differs from zero.