Confidence Intervals

Question

A random sample of 100 observations produced a mean of x¯=21.8 from a population with a normal distribution and a standard deviation σ=4.58. 

(a) Find a 99% confidence interval for 𝜇 

 ≤𝜇≤

(b) Find a 95% confidence interval for 𝜇 

 ≤𝜇≤

(c) Find a 90% confidence interval for 𝜇 

 ≤𝜇≤

Answer 1

We're sampling from a normal distribution so the sample mean x¯ is normal. The standard deviation for the sample mean is 4.58/√100 = .458

a) 20.62 ≤ μ ≤ 22.98

This interval is centered at the sample mean 21.8. The width of the interval is such that the right-hand and left-hand tail probabilities are both .5%

b) 20.90 ≤ μ ≤ 22.70

Right-hand and left-hand tail probabilities were both set to 2.5%

c) 21.05 ≤ μ ≤ 22.55

Right-hand and left-hand tail probabilities were both set to 2.5%

The evaluations were done using R. I rounded to two decimal places.