In an article in the Journal of Management Information Systems, Mahmood and Mann investigate how information technology (IT) investment relates to company performance. In particular, Mahmood and Mann obtain sample data concerning IT investment for companies that use information systems effectively. Among the variables studied are the company's IT budget as a percentage of company revenue, percentages of the IT budget spent on staff and training, and number of PCs and terminals as a percentage of total employees.

a. Suppose a random sample of 15 companies considered to use the information systems effectively yields a sample mean IT budget as a percentage of company revenue of x¯ = 2.73 with a standard deviation of s = 1.64. Assuming that IT budget percentages are approximately normally distributed, calculate a 99 percent confidence interval for the mean IT budget as a percentage of company revenue for all firms that use information systems effectively. Does this interval provide evidence that a firm can successfully use information systems with an IT budget that is less than 5 percent of company revenue? Explain.

b. Suppose a random sample of 15 companies considered to use information systems effectively yields a sample mean number of PCs and terminals as a percentage of total employees of x¯= 34.76 with a standard deviation of s = 25.37. Assuming approximate normality, calculate a 99 percent confidence interval for the mean number of PCs and terminals as a percentage of total employees for all firms that use information systems effectively. Why is this interval so wide? What can we do to obtain a narrower (more useful) confidence interval?