Question

A 95% confidence interval for a population mean is given as 32.2 < μ < 42.0. Round your answers to 1 decimal place.

(a) Calculate the sample mean. x =

(b) Calculate the margin of error. E =

Answer 1

Solution:

Given a 95% confidence interval for mean is 32.2 < μ < 42.0

We know , confidence interval for mean is given by

sample mean margin of error

So ,

Lower Limit = sample mean - margin of error

Upper Limit = sample mean + margin of error

Solving these two equations , we can say that

Sample mean = (Upper Limit + Lower Limit)/2

Margin of error = (Upper Limit - Lower Limit)/2

a)

Sample mean = (Upper Limit + Lower Limit)/2 = (42.0 + 32.2)/2 = 37.1

Sample mean = 37.1

b)

Margin of error = (Upper Limit -  Lower Limit)/2 = (42.0 + 32.2)/2 = 4.9

Margin of error E = 4.9