Question

•Let’s say Joe measures the average cross section area of pvc piping to be 20 millimeters squared for a sample of 64. The company knows historically, the area of the pvc piping is 18 millimeters squared. Joe knows the population sample standard deviation to be 10 millimeter squares. Construct a 95% and 90% Confidence interval of the situation.

a.) Calculate the 90% and 95% confidence intervals?

b.) What are the Margin of errors for 90% confidence and 95% confidence? Which one has a wider margin of error?

c.) Calculate the sample size required to get only a margin of error of 0.001 for 95% confidence.

Answer 1

Answer)

As the population s.d is known here we can use standard normal z table to estimate the intervals

A)

Critical value z from z table for 90% confidence level is 1.645

Margin of error (MOE) = Z*S.D/√N = 1.645*10/√64 = 2.05625

Interval is given by

(Mean - MOE, Mean + MOE)

Mean = 20

(17.94375, 22.05625)

Critical value z from z table for 95% confidence level is 1.96

Moe = 1.96*10/√64 = 2.45

(17.55, 22.45)

B)

Margin of error for 90% confidence level is 2.05625

Margin of error for 95% confidence level is 2.45

95% confidence level has wider interval

C)

0.001 = 1.96*10/√n

N = 384160000