1. According to the Census Bureau, 2,475,780 people are employed by the federal government in the United States (U.S. Census Bureau website, May 30, 2016).
Suppose that a random sample of 3500 of these federal employees was selected and the number of sick hours each of these employees took last year was collected
from an electronic personnel database. The data collected in this survey are provided in the DATAfile named ​FedSickHours​. Based on historical data, the
population standard deviation can be assumed to be known with .
● What is the point estimate for the mean number of sick hours taken by federal employees last year?
● Using 99% confidence, what is the margin of error?
● Using the results from part (a) and part (b), develop the 99% confidence interval estimate of the mean number of sick hours taken by federal employees last year.
● If the mean sick hour’s federal employees took two years ago was 62.2, what would the confidence interval in part (c) lead you to conclude about last year?
2. ABC News reports that 58% of U.S. drivers admit to speeding (ABC News website, May 27, 2016). Suppose that new satellite technology can instantly measure
the speed of any vehicle on a U.S. road and determine whether the vehicle is speeding, and this satellite technology was used to take a sample of 20,000 vehicles at
6:00 p.m. EST on a recent Tuesday afternoon. Of these 20,000 vehicles, 9252 were speeding.
● What is the point estimate for the proportion of vehicles on U.S. roads that speed?
● Using 99% confidence, what is the margin of error?
● Using the results from part (a) and part (b), develop the 99% confidence interval estimate of the proportion of vehicles on U.S. roads that speed.
● What the confidence interval in part (c) lead you to conclude about the ABC News report?