Question

The breaking strengths of cables produced by a certain manufacturer have a standard deviation of 83 pounds. A random sample of 80 newly manufactured cables has a mean breaking strength of 1900 pounds. Based on this sample, find a 99% confidence interval for the true mean breaking strength of all cables produced by this manufacturer. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

What is the lower limit of the 99% confidence interval?
What is the upper limit of the 99% confidence interval?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 1900

Population standard deviation =    = 83

Sample size = n = 80

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576

Margin of error = E = Z/2 * ( /n)

= 2.576 * ( 83 /  80 )

= 23.9

At 99% confidence interval estimate of the population mean is,

  ± E

1900 ± 23.9

( 1876.1, 1923.9)  

lower limit = 1876.1

upper limit = 1923.9