Question

The union for a particular industry has determined that the standard deviation of the daily wages of its workers is $21. A random sample of 50 workers in this industry has a mean daily wage of $118. Find a 90% 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. What is the lower limit of the 90% confidence interval? $0 What is the upper limit of the 90% confidence interval? SD 5 ?

Answer 1

1) Here we have: X = 118 o = 21 n = 50 a = 1-0.90 = 0.10 (90% confidence level) Critical value: Icrit= Za 12 = 20.10/2 = +1.645 Confidence interval: A = x+zc $19 21 = 118 + 1.645 * 150

= 118 + 4.9 = 113.1 < u < 122.9 The lower limit of the 90% confidence interval = $113.1 The upper limit of the 90% confidence interval= $122.9