Answer:
Step-by-step explanation:
For before,
Mean, x1 = (56 + 27 + 23 + 28 + 27 + 34 + 54 + 50 + 28 + 21)/10 = 34.8
Standard deviation = √(summation(x - mean)²/n
n = 10
Summation(x - mean)² = (56 - 34.8)^2 + (27 - 34.8)^2 + (23 - 34.8)^2 + (28 - 34.8)^2 + (27 - 34.8)^2 + (34 - 34.8)^2 + (54 - 34.8)^2 + (50 - 34.8)^2 + (28 - 34.8)^2 + (21 - 34.8)^2 = 1593.6
Standard deviation = √(1593.6/10
s1 = 12.62
For after,
Mean, x1 = (60 + 45 + 31 + 39 + 39 + 36 + 58 + 60 + 38 + 29)/10 = 43.5
Summation(x - mean)² = (60 - 43.5)^2 + (45 - 43.5)^2 + (31 - 43.5)^2 + (39 - 43.5)^2 + (39 - 43.5)^2 + (36 - 43.5)^2 + (58 - 43.5)^2 + (60 - 43.5)^2 + (38 - 43.5)^2 + (29 - 43.5)^2 = 1250.5
Standard deviation = √(1250.5/10
s2 = 11.18
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
For a 90% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (10 - 1) + (10 - 1) = 18
z = 1.734
The point estimate is
x1 - x2 = 34.8 - 43.5 = - 8.7
Margin of error = z√(s1²/n1 + s2²/n2) = 1.734√(12.62²/10 + 11.18²/10) = 8.5
Confidence interval = - 8.7 ± 8.5