Question

The Interstate Conference of Employment Security Agencies says the average workweek in the United States is down to only 35 hours, largely because of a rise in part-time workers. Suppose this figure was obtained from a random sample of 20 workers and that the standard deviation of the sample was 4.3 hours. Assume hours worked per week are normally distributed in the population. Use this sample information to develop a 90% confidence interval for the population variance of the number of hours worked per week for a worker. Interpret your interval.

Answer 1

Solution-

We have given

Sample size n = 20

Sample standard deviation s =4.3

Sample variance s² = 4.3² = 18.49

Significance level = 90%

90% confidence interval for the population variance of the number of hours worked per week for a worker is

11.66 < σ2 < 34.73 ....( Rounded to 2 decimals)

• Calculations