Question

1. (8.1) You draw a sample of size 30 from a normally distributed population with a standard deviation of 4. The sample mean is 41.

a. If you want to construct a 95% confidence interval, how much probability will be in each tail of the distribution?

b. Find the margin of error for a 95% confidence interval.

c. Construct and write a statement interpreting a 95% confidence interval.

Answer 1

a)
Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Each tail has 0.025 probability

b)
ME = zc * σ/sqrt(n)
ME = 1.96 * 4/sqrt(30)
ME = 1.43

c)
CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (41 - 1.96 * 4/sqrt(30) , 41 + 1.96 * 4/sqrt(30))
CI = (39.57 , 42.43)

One can be 95% confident that the true population mean will be between 39.57 and 42.43