Question

5. A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x is found to be 108, and the standard deviation, s, is found to be 10. a. Find the degrees of freedom about u if the sample size, n, is 23. b. Construct a 95% confidence interval about u if the sample size, n is 27. brud on C. How does increasing the sample size affect the margin of error, E?

Answer 1

a)
df = 23 - 1 = 22

b)
sample mean, xbar = 108
sample standard deviation, s = 10
sample size, n = 27
degrees of freedom, df = n - 1 = 26

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.056

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (108 - 2.056 * 10/sqrt(27) , 108 + 2.056 * 10/sqrt(27))
CI = (104.04 , 111.96)

c)
increasing the sample size will decrease ME