A company's cost-to-income ratio is a measure of its ability to control its costs. The lower the ratio (expressed as a percentage), the better the company's ability is to control its cost. An analyst recorded the cost-to-income ratio (as a percentage) of 50 randomly selected public companies to study their ability to control their operating cost. Assume that cost-to-income ratios across public companies are normally distributed.
(a) Compute the mean (average) and standard deviation of the sample of the cost- to-income ratios using the Descriptive Statistics option in Data Analysis. Interpret the profile of this measure across the sample of public companies surveyed.
(b) Find the 95% confidence interval for the mean cost-to-income ratio for all public companies. (Hint: Tick the Confidence Level for Mean box in Descriptive Statistics).
(c) Re-compute and confirm the 95% confidence limits using the TINV formula to find the t-limits.
(d) As a rule of thumb, a public company's cost-to-income ratio should not exceed 75%. Use the TDIST formula and the sample evidence from (a) to determine what percentage of all public companies are likely to be in violation of the rule of thumb.