Over the years, there has been a rapid rise of fees and expenses charged by mutual funds. A random sample of 12 stock funds gives a mean annual expense of 1.63% with a standard deviation of 0.24% and coefficient of skewness of 0.01 and coefficient of kurtosis of -0.8. An independent random sample of 12 municipal bond funds gives a mean annual expense of 0.89% with a standard deviation of 0.23% and coefficient of skewness and kurtosis as 0.07 and 0.056 respectively. It is desired to to check if the mean annual expense for municipal bond funds is lesser than the mean annual expense for the stock funds.
(a) Set up the relevant null and alternative hypothesis.
(b) Write down the test statistic to be used for testing the hypothesis.
(c) What is the sampling distribution of the test statistic if the null hypothesis is true?
(d) If the level of significance α = 1%, write down the critical value.
(e) Based on the data, do you reject the null hypothesis? Justify.
(f) Did you commit a type II error based on your conclusion to 3e above?