Annual holdings turnover for a mutual fund is the percentageof a funds assets that are

Chapter 8, Problem 64

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Annual holdings turnover for a mutual fund is the percentageof a funds assets that are sold during a particularyear. Generally speaking, a fund with a low value ofturnover is more stable and risk averse, whereas a highvalue of turnover indicates a substantial amount of buyingand selling in an attempt to take advantage of short-termmarket fluctuations. Here are values of turnover for asample of 20 large-cap blended funds (refer to Exercise1.53 for a bit more information) extracted fromMorningstar.com:1.03 1.23 1.10 1.64 1.30 1.27 1.25 0.78 1.05 0.640.94 2.86 1.05 0.75 0.09 0.79 1.61 1.26 0.93 0.84a. Would you use the one-sample t test to decidewhether there is compelling evidence for concludingthat the population mean turnover is less than 100%?Explain.b. A normal probability plot of the 20 ln(turnover) valuesshows a very pronounced linear pattern, suggestingit is reasonable to assume that the turnover distributionis lognormal. Recall that X has a lognormaldistribution if ln(X) is normally distributed withmean value m and variance s2. Because m is also themedian of the ln(X) distribution, em is the median ofthe X distribution. Use this information to decidewhether there is compelling evidence for concludingthat the median of the turnover population distributionis less than 100%.