Answer:
95% confidence interval for the average net change is between a lower limit of 11.709 and an upper limit of 30.921.
The critical value that should be used in constructing the confidence interval is 4.303.
Step-by-step explanation:
Confidence interval is given as mean +/- margin of error (E)
mean = (17+20+26)/3 = 63/3 = 21
sd = sqrt[((17-21)^2 + (20-21)^2 + (26-21)^2) ÷ 3] = sqrt(42÷3) = sqrt(14) = 3.74
n = 3
degree of freedom = n-1 = 3-1 = 2
confidence level (C) = 95% = 0.95
significance level = 1 - C = 1 - 0.95 = 0.05 = 5%
critical value (t) corresponding to 2 degrees of freedom and 5% significance level is 4.303.
The critical value is 4.303
E = t×sd/√n = 4.303×3.74/√3 = 9.291
Lower limit of mean = mean - E = 21 - 9.291 = 11.709
Upper limit of mean = mean + E = 21 + 9.291 = 30.291
95% confidence interval is (11.709, 30.391)
