A recent article describes the success of business schools in Europe and the demand on that continent for the MBA degree. The article reports that a survey of 280 European business positions resulted in the conclusion that only one-seventh of the positions for MBAs at European businesses are currently filled. Assuming that these numbers are exact and that the sample was randomly chosen from the entire population of interest, give a 90% confidence interval for the proportion of filled MBA positions in Europe.
Solution: We want to find a 90% confidence interval for the proportion of filled MBA positions in Europe. This problem corresponds technically to the problem of finding a confidence interval for a population proportion. In this case, we have the following expression for the confidence interval
whererepresents the sample proportion. For a 90% confidence interval we have , which means that . Therefore, the confidence interval is