Discuss the following problems:
Q1. The 1996-97 mean annual starting salary for accounting majors was $30,393 (U.S. News On-line. December 28, 1997). Assume that for the population of graduates with accounting majors the mean annual starting salary is pr = $30,393 and the standard deviation is 0 = $2000.
a. What is the probability that a simple random sample of accounting graduates will have a sample mean within $5250 of the population mean for each of the following sample sizes: 30, 50, 100, 200, and 400?
b. What is the advantage of a larger sample size when attempting to estimate a population mean?
Q2. The U.S. Bureau of Labor Statistics reported the mean hourly wage rate for individuals in executive, administrative, and managerial occupations is $24.07 (The Wall Street Journal Almanac 1998). Assume the population mean is ,u = $24.07 and the population standard deviation is o = $4.80. A sample of 120 individuals in executive, administrative, and managerial occupations will be selected.
a. What is the probability that the sample mean will be within 0.50 of the population mean?
b. What is the probability that the sample mean will be within as 1.00 of the population mean?
Q3. A researcher reports survey results by stating that the standard error of the mean is 20. The population standard deviation is 500.
a. How large was the sample used in this survey?
b. What is the probability that the estimate would be within :25 of the population mean?