Question

A sample of 21 paired observations generates the following data: d = 1.0 and 5 = 2.8. Assume a normal distribution. (You may find it useful to reference the appropriate table: z table or table) a. Construct the 99% confidence interval for the mean difference HD (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Confidence interval is b. Using the confidence interval, test whether the mean difference differs There is no evidence that the mean difference differs from zer nces There is evidence that the mean difference differs from zero.

Answer 1

Answer)

Given info

d = 1

S.d = √2.8

N = 21

As the population s.d is unknown we will use t distribution to estimate the interval

Degrees of freedom is = n-1 = 20

For 20 df and 99% confidence level, critical value t from t table is = 2.85

Margin of error (MOE) = t*s d/√n = 2.85*√2.8/√21 = 1.04

Confidence interval is given by

Mean - moe to mean + moe

-0.04 to 2.04

Null hypothesis Ho : u1-u2 = 0

Alternate hypothesis Ha : u1-u2 not equal to 0

As the interval contains 0

We fail to reject the null hypothesis Ho

There is no evidence that mean difference differs from 0