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.
Jon Jacobson, an overzealous graduate student, has just completed a first draft of his 700-page dissertation. Jon has typed his paper himself and is interested in knowing the average number of typographical errors per page, but does not want to read the whole paper. Knowing a little bit about business statistics, Jon selected 40 pages at random to read and found that the average number of typos per page was 4.3 and the sample standard deviation was 1.2 typos per page.
- Calculate the estimated standard error of the mean
- Construct for Jon a 90 percent confi dence interval for the true average number of typos per page in his paper.
The Nebraska Cable Television authority conducted a test to determine the amount of time people spend watching television per week. The NCTA surveyed 84 subscribers and found the average number of hours watched per week to be 11.6 hours and the standard deviation to be 1.8 hours.
- What is the estimated population standard deviation for this population? (There are about95,000 people with cable television in Nebraska.
- Calculate the estimated standard error of the mean..
- Construct a 98 percent confi dence interval for the population 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
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?
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.