Question

The union for a particular industry has determined that the standard deviation of the daily wages of its workers is $

19

. A random sample of

150

workers in this industry has a mean daily wage of $

112

. Find a

99%

confidence interval for the true mean daily wage of all union workers in the industry. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

WHAT THE LOWER LIMIT OF 99% CONFIDENCE INTERVAL?

WHAT THE UPPER LIMIT OF 99% CONFIDENCE INTERVAL

Answer 1

Given the population standard deviation and sample mean as . The sample size is  .

Since the sample size is large (>25) and population standard deviation is known, we use normal distribution for finding the confidence interval.

The two sided confidence interval for mean based on the sample data is

When , the 99% CI for population means is

Thus,

THE LOWER LIMIT OF 99% CONFIDENCE INTERVAL is

THE UPPER LIMIT OF 99% CONFIDENCE INTERVAL is