The West view High School nurse is interested in knowing the average height of seniors at this school, but she does not have enough time to examine the records of all 430 seniors. She randomly selects 48 students. She finds the sample mean to be 64.5 inches and the standard deviation to be 2.3 inches.
- Find the estimated standard error of the mean.
- Construct a 90 percent confi dence interval for the 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.
Joel Fried lander is a broker on the New York Stock Exchange who is curious about the amount of time between the placement and execution of a market order. Joel sampled 45 orders and found that the mean time to execution was 24.3 minutes and the standard deviation was 3.2 minutes. Help Joel by constructing a 95 percent confi dence interval for the mean time to execution
Chief of Police Kathy Ackert has recently instituted a crackdown on drug dealers in her city. Since the crackdown began, 750 of the 12,368 drug dealers in the city have been caught. The mean dollar value of drugs found on these 750 dealers is $250,000. The standard deviation of the dollar value of drugs for these 750 dealers is $41,000. Construct for Chief Ackert a 90 percent confidence interval for the mean dollar value of drugs possessed by the city’s drug dealers.
Oscar T. Grady is the production manager for Citrus Groves Inc., located just north of Ocala, Florida. Oscar is concerned that the last 3 years’ late freezes have damaged the 2,500 orange trees that Citrus Groves owns. In order to determine the extent of damage to the trees, Oscar has sampled the number of oranges produced per tree for 42 trees and found that the average production was 525 oranges per tree and the standard deviation was 30 oranges per tree
- Estimate the population standard deviation from the sample standard deviation
- Estimate the standard error of the mean for this fi nite population.
- Construct a 98 percent confi dence interval for the mean per-tree output of all 2,500 trees
- If the mean orange output per tree was 600 oranges 5 years ago, what can Oscar say about the possible existence of damage now?