You have heard that if you leave your money in mutual funds for a longer period of time, you will see a greater return. So you would like to compare the $3-$year and $5-$year returns of a random sample of mutual funds to see if indeed, your return is expected to be greater if you leave your money in the fund for $5$ years. Complete parts a and $b$ below. Assume a significance level of $=0\mathrm{.}05.$

Click the icon to view, the $3-$year and $5-$year returns of the mutual funds.