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

**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.)**

**c)****Calculate a 90 percent confidence interval for
the difference between the mean annual expenses for stock funds and municipal
bond funds. Can we be 90 percent confident that the mean annual expense for
stock funds exceeds that for municipal bond funds by more than 0.5 percent?****(Round your answer to
4 decimal places and other answers to 3 decimal places.)**

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