Chapter 7
Problem 1. A sample of 50 Fortune 500 companies showed 5 were based in New York, 6 in California, 2 in Minnesota, and 1 in Wisconsin.
Develop an estimate of the proportion of Fortune 500 companies based in New York.
Develop an estimate of the number of Fortune 500 companies based in Minnesota.
Develop an estimate of the proportion of Fortune 500 companies that are not based in these four states.
Problem 2.The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT):
Critical Reading 502
Mathematics 515
Writing 494
Assume that the population standard deviation on each part of the test is σ = 100.
What is the probability a random sample of 81 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test?
What is the probability a random sample of 81 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test? Compare this probability to the value computed in part (a).
What is the probability a random sample of 100 test takers will provide a sample mean test score within 10 of the population mean of 494 on the writing part of the test? Comment on the differences between this probability and the values computed in parts (a) and (b).
Problem 3.To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected.
Would you use the finite population correction factor in calculating the standard error of the mean? Explain.
If the population standard deviation is σ = 8.2 years, compute the standard error both with and without the finite population correction factor. What is the rationale for ignoring the finite population correction factor whenever n/N <= .05?
c. What is the probability that the sample mean age of the employees will be within 2 years of the population mean age?