# An article in Fortune magazine reported on the rapid rise of fees and expenses c

**Question description**

An article in *Fortune* magazine
reported on the rapid rise of fees and expenses charged by mutual funds.
Assuming that stock fund expenses and municipal bond fund expenses are each
approximately normally distributed, suppose a random sample of 12 stock funds
gives a mean annual expense of 1.60 percent with a standard deviation of 0.33
percent, and an independent random sample of 12 municipal bond funds gives a
mean annual expense of 0.88 percent with a standard deviation of 0.20 percent.
Let *µ*_{1} be the mean annual expense for stock funds,
and let *µ*_{2} be the mean annual expense for municipal
bond funds. Do parts *a*, *b*, and *c* by using
the equal variances procedure.

a)
Set up the null and
alternative hypotheses needed to attempt to establish that the mean annual
expense for stock funds is larger than the mean annual expense for municipal
bond funds. Test these hypotheses at the 0.10 level of significance.**(Round your s_{p}^{2}answer to 4 decimal places andt-value to 3 decimal places.)**

**b)
**Set up the
null and alternative hypotheses needed to attempt to establish that the mean
annual expense for stock funds exceeds the mean annual expense for municipal
bond funds by more than 0.5 percent. Test these hypotheses at the 0.10 level of
significance.**(Round your t-value
to 3 decimal places**

**and other answers to 1 decimal place.)**

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