From a population with known standard deviation of 1.65, a sample of 32 items resulted in 34.8 as an estimate of the mean.
- Find the standard error of the mean.
- Compute an interval estimate that should include the population mean 99.7 percent of the time.
The University of North Carolina is conducting a study on the average weight of the many bricks that make up the University’s walkways. Workers are sent to dig up and weigh a sample of 421 bricks and the average brick weight of this sample was 14.2 lb. It is a well-known fact that the standard deviation of brick weight is 0.8 lb.
- Find the standard error of the mean.
- What is the interval around the sample mean that will include the population mean 95.5 percent of the time?
Because the owner of the Bard’s Nook, a recently opened restaurant, has had difficulty estimating the quantity of food to be prepared each evening, he decided to determine the mean number of customers served each night. He selected a sample of 30 nights, which resulted in a mean of 71. The population standard deviation has been established as 3.76.
- Give an interval estimate that has a 68.3 percent probability of including the population mean.
- Give an interval estimate that has a 99.7 percent chance of including the population mean.
The manager of the Neuse River Bridge is concerned about the number of cars “running” the toll gates and is considering altering the toll-collection procedure if such alteration would be cost-effective. She randomly sampled 75 hours to determine the rate of violation. The resulting average violations per hour was 7. If the population standard deviation is known to be 0.9, estimate an interval that has a 95.5 percent chance of containing the true mean.
Gwen Taylor, apartment manager for Willow Wood Apartments, wants to inform potential renters about how much electricity they can expect to use during August. She randomly selects 61 residents and discovers their average electricity usage in August to be 894 kilowatt hours (kwh). Gwen believes the variance in usage is about 131 (kwh)2.
- Establish an interval estimate for the average August electricity usage so Gwen can be 68.3 percent certain the true population mean lies within this interval.
- Repeat part (a) with a 99.7 percent certainty.
- If the price per kwh is $0.12, within what interval can Gwen be 68.3 percent certain that the average August cost for electricity will lie?
The school board of For sight County considers its most important task to be keeping the average class size in For sight County schools less than the average class size in neighboring Hindsight County. Miss Dee Marks, the school superintendent for For sight County, has just received reliable information indicating that the average class size in Hindsight County this year is 30.3 students. She does not yet have the figures for all 621 classes in her own school system, so Dee is forced to rely upon the 76 classes that have reported class sizes, yielding an average class size of 29.8 students. Dee knows that the class size of For sight County classes has a distribution with an unknown mean and standard deviation equal to 8.3 students. Assuming that the sample of 76 that Miss Marks possesses is randomly chosen from the population of all For sight County class sizes:
- Find an interval that Dee can be 95.5 percent certain will contain the true mean.
- Do you think that Dee has met her goal?
- If the price per kwh is $0.12, within what interval can Gwen be 68.3 percent certain that the average August cost for electricity will lie?
From a population of 540, a sample of 60 individuals is taken. From this sample, the mean is found to be 6.2 and the standard deviation 1.368.
- Find the estimated standard error of the mean.
- Construct a 96 percent confidence interval for the mean.
- If the price per kwh is $0.12, within what interval can Gwen be 68.3 percent certain that the average August cost for electricity will lie?
In an automotive safety test conducted by the North Carolina Highway Safety Research Center, the average tire pressure in a sample of 62 tires was found to be 24 pounds per square inch, and the standard deviation was 2.1 pounds per square inch.
- What is the estimated population standard deviation for this population? (There are about a million cars registered in North Carolina.)
- Calculate the estimated standard error of the mean
- Construct a 95 percent confi dence interval for the population mean
The manager of Cardinal Electrics light bulb division must estimate the average number of hours that a light bulb made by each light bulb machine will last. A sample of 40 light bulbs was selected from machine A and the average burning time was 1,416 hours. The standard deviation of burning time is known to be 30 hours.
- Compute the standard error of the mean.
- Construct a 90 percent confi dence interval for the true population mean.
Upon collecting a sample of 250 from a population with known standard deviation of 13.7, the mean is found to be 112.4.
- Find a 95 percent confidence interval for the mean.
- Find a 99 percent confi dence interval for the mean.