Statistics Problem Set: Scanning Errors at Wal-Mart

5.60 It costs you $10 to draw a sample of siz n = 1 and measure the attribute of interest. You have a budget of $1,500.
a. Do you have sufficient funds to estimate the population mean for the attribute of interest with a 95% confidence interval 5 units in width? Assume sigma = 14.
b. If you used a 90% confidence level, would you answer to part a change?

5.64 Accounting and Machiavellianism. Refer to the Behavioural Research in Accounting (Jan. 2008) study of Machiavellian traits in accountants, where a Mach rating score was determined for each in a sample of accounting alumni who work as purchasing managers. Suppose you want to reduce the width of the 95% confidence interval for the true mean Mach rating score of all purchasing managers you obtained. How many purchasing managers should be included in the sample if you desire a sampling error of only 1.5 Mach rating points? (use sigma = 12 in your calculations).

5.66 "Made in the USA" survey. Determine what "Made in the USA" means to consumers. Recall that 64 of 106 shoppers at a shopping mall in Muncie, Indiana, believe that "Made in the USA" implies all labor and materials are produced in the United States. Suppose the researchers want to increase the sample size in order to estimate the true proportion, p, to within .05 of its true value using a 90% confidence interval.
a. What is the confidence level desired by the researchers?
b. What is the sampling error desired by the researchers?
c. Compute the sample size necessary to obtain the desired estimate.

5.68 Scanning errors at Wal-Mart. In a sample of 60 Wal-Mart stores, 52 violated the NIST scanner accuracy standard. The conditions for a valid large-sample confidence interval for the true proportion of Wal-Mart stores in California that violate the NIST standard were not met. Determine the number of Wal-Mart stores that must be sampled in order to estimate the true proportion to within 0.05 with 90% confidence using the large-sample method.