Question

Construct a confidence interval for μd, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed. A test of writing ability is given to a random sample of students before and after they completed a formal writing course. The results are given below. Construct a​ 99% confidence interval for the mean difference between the before and after scores.
Before 70 80 92 99 93 97 76 63 68 71 74
After 69 79 90 96 91 95 75 64 62 64 76

Answer 1

Answer:

Step-by-step explanation:

Group Before After

Mean 80.27 78.27

SD 12.76 12.92

SEM 3.85 3.89

N 11 11

df = 10

standard error of difference = 0.798

The mean of Before minus After equals 2.00

Given a=0.01, |t(0.005, df=10)|=3.17 (check student t table)

So 99% CI is

2±t*s

--> 2±3.17*0.798

--> -0.5 < µd< 4.5

Answer:-0.5 < µd< 4.5