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?
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?
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 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.
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 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?
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.
From a population known to have a standard deviation of 1.4, a sample of 60 individuals is taken. The mean for this sample is found to be 6.2.
- Find the standard error of the mean.
- Establish an interval estimate around the sample mean, using one standard error of the mean.
Eunice Gunterwal is a frugal undergraduate at State U. Who is interested in purchasing a used car. She randomly selected 125 want ads and found that the average price of a car in this sample was $3,250. Eunice knows that the standard deviation of used-car prices in this city is $615
- Establish an interval estimate for the average price of a car so that Eunice can be 68.3 percent certain that the population mean lies within this interval.
- Establish an interval estimate for the average price of a car so that Miss Gunterwal can be 95.5 percent certain that the population mean lies within this interval.
For a population with a known variance of 185, a sample of 64 individuals leads to 217 as an estimate of the mean.
- Find the standard error of the mean.
- Establish an interval estimate that should include the population mean 68.3 percent of the time.