Chapter 8, Problem 64SE

Annual holdings turnover for a mutual fund is the percentage of a fund’s assets that are sold during a particular year. Generally speaking, a fund with a low value of turnover is more stable and risk averse, whereas a high value of turnover indicates a substantial amount of buying and selling in an attempt to take advantage of short-term market fluctuations. Here are values of turnover for a sample of 20 large-cap blended funds (refer to Exercise 1.53 for a bit more information) extracted from Morningstar.com:

1. a. Would you use the one-sample t test to decide whether there is compelling evidence for concluding that the population mean turnover is less than 100%? Explain.
2. b. A normal probability plot of the 20 ln(turnover) values shows a very pronounced linear pattern, suggesting it is reasonable to assume that the turnover distribution is lognormal. Recall that X has a lognormal distribution if In(X) is normally distributed with mean value μ and variance σ². Because μ, is also the median of the ln(X) distribution, e^μ is the median of the X distribution. Use this information to decide whether there is compelling evidence for concluding that the median of the turnover population distribution is less than 100%.