Question

A sample of 20 paired observations generates the following data: d− = 1.3 and s2D = 2.6. Assume a normal distribution. (You may find it useful to reference the appropriate table: z table or t table) a. Construct the 90% confidence interval for the mean difference μD. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) 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

Using excel function CONFIDENCE.T to find the margin of error for the 90% confidence interval

margin of error (E) = CONFIDENCE.T(alpha,standard deviation, size)

seting alpha = 1- 0.90 = 0.10, standard deviation = sqrt(2.6), size n = 20

we get

E = CONFIDENCE.T(0.10,sqrt(2.6), 20)

= 0.6234

(A) confidence interval =

(B) There is evidence that the mean difference differs from zero.

because the confidence interval does not include the null value of 0, this means that the mean difference is significantly different from 0.