Question

The makers of a soft drink want to identify the average age of its consumers. A sample of 55 consumers was taken. The average age in the sample was 21 years with a standard deviation of 4 years.

a. Construct a 95% confidence interval for the true average age of the consumers.

b. Construct an 80% confidence interval for the true average age of the consumers.

c. Discuss why the 95% and 80% confidence intervals are different.

Answer 1

Confidence interval, CI = Z*

= 21 years

s = 4 years

n = 55

a) For 95% confidence level, Z* = 1.96

Confidence interval = 21 1.96 x

= 21 1.057

= (19.943, 22.057)

b) For 80% confidence level, Z* = 1.28

Confidence interval = 21 1.28 x

= 21 0.690

= (20.310, 21.690)

c) 95% confidence interval means that, we are 95% confident that the interval will contain the true population mean. In 80% confidence interval, we are only 80% confident about the same. As confidence level increases, to be more sure that the interval will contain the population mean, the width of confidence interval increases.