Question

Construct a confidence interval for mu Subscript d 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

Before	70	80	92	99	93	97	76	63	68	71	74
After	69	79	90	96	91	95	75	64	62	64	76
Before-After	1	1	2	3	2	2	1	-1	6	7	-2

sample mean, xbar = 2
sample standard deviation, s = 2.6458
sample size, n = 11
degrees of freedom, df = n - 1 = 10

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 3.169

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (2 - 3.169 * 2.6458/sqrt(11) , 2 + 3.169 * 2.6458/sqrt(11))
CI = (-0.528 , 4.528)