Discuss the below problems:
Q1. What is sampling error? Could the value of the sampling error be zero? If it were zero, what would this mean?
Q2. List the reasons for sampling. Give an example of each reason for sampling.
Q3. 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.
a. If we select a random sample of 50 households, what is the standard error of the mean?
b. What is the expected shape of the distribution of the sample mean?
c. What is the likelihood of selecting a sample with a mean of at least $112,000?
d. What is the likelihood of selecting a sample with a mean of more than $100,000?
e. Find the likelihood of selecting a sample with a mean of more than $100,000 but less than $112,000.
Q4. 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.
a. What is the estimated population mean?
b. Determine a 95 percent confidence interval for the population mean.
Q5. 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
Q6. 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?
Business Research Methods
Q7. You have been approached by the editor of Gentlemen's Magazine to carry out a research study. The magazine has been unsuccessful in attracting shoe manufacturers as advertisers. When the sales force tried to secure advertising from shoe manufacturers, they were told men's clothing stores are a small and dying segment of their business. Since Gentlemen's Magazine goes chiefly to men's clothing stores, the manufacturers reasoned that it was, therefore, not a good vehicle for their advertising. The editor believes that a survey (via mail questionnaire) of men's clothing stores in the United States will probably show that these stores are important outlets for men's shoes and are not declining in importance as shoe outlets. He asks you to develop a proposal for the study and submit it to him. Develop the management-research question hierarchy that will help you to develop a specific proposal.