Confidence interval

Question

A sample of size =n70  is drawn from a normal population whose standard deviation is =σ 8.2. The sample mean is x= 49.35

(a) Construct an 

80%  confidence interval for the mean

Answer 1

A two-sided confidence interval of a sample mean estimate, say x_bar, for a population estimate, mu, is of the form

(x_bar - z_{1-alpha/2} * sqrt(s^2/n), x_bar + z_{1-alpha/2} * sqrt(s^2/n)

where s^2 is the sample variance (which can be replaced with the population variance sigma^2 if known), n is the sample size, and z_{1-alpha/2} is the z-score that gives the probability P(Z < |z|) = 1-alpha/2.

For the probability to be 80%, we use alpha=0.4. This value can be found in a z-table.