Question

We want to know the mean number of hours worked on a weekend day, among those who work weekends. Suppose that a simple random sample of size 1015 from the target population produced a sample mean of 5.2 hours. Further suppose that the sample standard deviation was 1.6. (a) What are the end points of a 90% confidence-interval estimate for the population mean? (Round to 2 digits after the decimal place.) [ , ] (b) What are the end points of a 95% confidence-interval estimate for the population mean? (Round to 2 digits after the decimal place.) [ , ] (c) What are the end points of a 99% confidence-interval estimate for the population mean? (Round to 2 digits after the decimal place.) [ , ]

Answer 1

a) At 90% confidence level, the critical value is z_0.05 = 1.645

The 90% confidence interval is

= 5.12, 5.28

b) At 95% confidence level, the critical value is z_0.025 = 1.96

The 95% confidence interval is

= 5.102, 5.298

= 5.10, 5.30

At 99% confidence level, the critical value is z_0.005 = 2.58

The 99% confidence interval is

= 5.07, 5.33