Question

10-9. A sample of 20 paired observations generates the following data: d−d− = 1.3 and s2DsD2 = 2.6. Assume a normal distribution. (You may find it useful to reference the appropriate table: z table or t table)

a. Construct the 99% 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:

Given that n = 20

= 1.3

Standard deviation s = √2.6 = 1.6125

Degrees of freedom df = n-1 = 20-1 = 19

  = 2.8609

a. The 99% confidence interval for the mean difference μ_{D is}

CI = ( - s/√n , + s/√n)

= [1.3 - 2.8609 (1.6125/ √20), 1.3 + 2.8609 (1.6125/ √20) ]

= (0.27, 2.33)   

b) since interval values are above 0 ,  The mean difference differs from zero.

There is evidence that the mean difference differs from zero.