91Ó°ÊÓ

A random sample is drawn from a population of unknown standard deviation. Construct a \(99 \%\) confidence interval for the population mean based on the information given. a. \(\quad n=49, x-17.1, s=2.1\) b. \(\quad n=169, x-=17.1, s=2.1\)

A government agency was charged by the legislature with estimating the length of time it takes citizens to fill out various forms. Two hundred randomly selected adults were timed as they filled out a particular form. The times required had mean 12.8 minutes with standard deviation 1.7 minutes. Construct a \(90 \%\) confidence interval for the mean time taken for all adults to fill out this form.

A sample of 250 workers aged 16 and older produced an average length of time with the current employer ("job tenure") of 4.4 years with standard deviation 3.8 years. Construct a \(99.9 \%\) confidence interval for the mean job tenure of all workers aged 16 or older.

The designer of a garbage truck that lifts roll-out containers must estimate the mean weight the truck will lift at each collection point. A random sample of 325 containers of garbage on current collection routes yielded \(x-=75.3 \mathrm{lb}, \mathrm{s}=12.8 \mathrm{lb}\). Construct a \(99.8 \%\) confidence interval for the mean weight the trucks must lift each time.

Wildlife researchers tranquilized and weighed three adult male polar bears. The data (in pounds) are: 926,742,1,109 . Assume the weights of all bears are normally distributed. a. Construct an \(80 \%\) confidence interval for the mean weight of all adult male polar bears using these data. b. Convert the three weights in pounds to weights in kilograms using the conversion \(1 \mathrm{lb}=0.453 \mathrm{~kg}\) (so the first datum changes to \((\mathrm{g} 26)(0.453)-410)\). Use the converted data to construct an \(80 \%\) confidence interval for the mean weight of all adult male polar bears expressed in kilograms. c. Convert your answer in part (a) into kilograms directly and compare it to your answer in (b). This illustrates that if you construct a confidence interval in one system of units you can convert it directly into another system of units without having to convert all the data to the new units.