Statistics

Jeanine Stewart QNT/561-Dr. J. Rudin-Instructor Homework Assignment-Individual Week 2 Chp 8. Exercise 21 What is a sampling error' Could the value of sampling error be zero' If it were zero what would this mean ' The sampling error is the difference between a population parameter and a sample statistic. The value of the sampling error could be zero but this would mean that we would have an exact representation of the population and that we knew all the characteristics of the entire population. Exercise 22 List the reasons for sampling' Give an example for each reason for sampling' Per the information in the chapter reading reasons for sampling involve to contact the whole population is time consuming (ex. A candidate running for national office- use of a poll and a few staff members are more efficient and can be done in 1 to 2 days versus years and lots of manpower to get this done.) Another reason is the cost of doing such a study of all the items in a population may be expensive. (Ex. Companies can test cereal, perfume cat food etc using $2,000 people in the population with a cost of approximately $40,000 versus studying 60 million people at a cost of about $1 billion). It is also physically impossible to check all the items in a population. (Ex. Attempting to check all the water in Lake Erie for bacterial levels is not physically capable but select water from a specific section of the lake.) The destructive nature of some tests. (If wine tasters drink all the wine in the winery to determine their vintage they would consume the entire crop and have nothing to sale). Finally, the sample results are adequate. (If the U.S. Government tested all the grocery stores in the population there is a very small chance that it would affect the price index versus using a small sample of stores). Exercise 34 1. Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $110,000. This distribution follows the normal distribution with a standard deviation of $40,000. If we select a random sample of 50 households, what is the standard error of the mean' Ans: =40,000/sqrt(50) 5656.854 What is the expected shape of the distribution of the sample mean' Ans: Normal What is the likelihood of selecting a sample with a mean of at least $112,000' Ans: 0.361817 What is the likelihood of selecting a sample with a mean of more than $100,000' Ans: 0.9615 Find the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000' Ans.: 0.599656 Chapter 9 Exercise 32 A state meat inspector in Iowa has been given the assignment of estimating the mean net weight of packages of ground chuck labeled “3 pounds.” Of course, he realizes that the weights cannot be precisely 3 pounds. A sample of 36 packages reveals the mean weight to be 3.01 pounds, with a standard deviation of 0.03 pounds. * What is the estimated population mean' Ans: 3.01 * Determine a 95 percent confidence interval for the population mean' Ans: 3.000 to 3.020 See Excel Worksheet Exercise 34 A recent survey of 50 executives who were laid off from their previous position revealed it took a mean of 26 weeks for them to find another position. The standard deviation of the sample was 6.2 weeks. Construct a 95 percent confidence interval for the population mean. Is it reasonable that the population mean is 28 weeks' Justify your answer. The confidence interval is 24.281 to 27.719. Since 29 weeks does not fall between the intervals it would not be reasonable to assume that the population mean is 28 weeks. See Excel Worksheet for calculation. Exercise 46 As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 220 applicants 14 failed the test. Develop a 99 percent confidence interval for the proportion of applicants that fail the test. Would it be reasonable to conclude that more than 10 percent of the applicants are now failing the test' In addition to the testing of applicants, Fashion Industries randomly tests its employees throughout the year. Last year in the 400 random tests conducted, 14 employees failed the test. Would it be reasonable to conclude that less than 5 percent of the employees are not able to pass the random drug test' The sample proportion is 14/220 = 0.0636 The confidence interval is: .0636 +/- 1.96 * sqrt(.0636*.9364/220) = (0.021, 0.106) Since the interval includes 10%, there is not enough evidence to suggest that the population proportion is not 10%. ----- The second sample proportion is 14/400 = 0.035 A 99% confidence interval is: 0.035 +/- 2.575 * sqrt(.035*.965/400) = (0.011, 0.059) So we do not have enough evidence to suggest that the true population proportion is not 5% because that value is in the interval. Chapter 3 Exercise 5