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:

1.03 1.23 1.10 1.64 1.30 1.27 1.25 0.78 1.05 0.64 0.94 2.86 1.05 0.75 0.09 0.79 1.61 1.26 0.93 0.84

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.

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 ln(X) is normally distributed with mean value m and variance s2

. Because m is also the median of the ln(X)

distribution, em 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%.