Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than $6 \%$. A mutual-fund rating agency randomly selects 26 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be $5.21 \%$. Is there sufficient evidence to conclude that the fund has moderate risk at the $\alpha=0.05$ level of significance? A normal probability plot indicates that the monthly rates of return are normally distributed.
What are the correct hypotheses for this test?
The null hypothesis is $\mathrm{H}_{0}$ :
The alternative hypothesis is $\mathrm{H}_{1}$ :

Step 1 ：Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 6%. A mutual-fund rating agency randomly selects 26 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 5.21%. Is there sufficient evidence to conclude that the fund has moderate risk at the \(\alpha=0.05\) level of significance? A normal probability plot indicates that the monthly rates of return are normally distributed.

Step 2 ：We are testing whether the standard deviation of the rate of return is less than 6%. The null hypothesis is that the standard deviation is equal to or greater than 6%, and the alternative hypothesis is that the standard deviation is less than 6%.

Step 3 ：The null hypothesis (H0) is that the standard deviation of the rate of return is equal to or greater than 6% (\(\sigma \geq 6\%\)).

Step 4 ：The alternative hypothesis (H1) is that the standard deviation of the rate of return is less than 6% (\(\sigma < 6\%\)).

Step 5 ：Final Answer: The null hypothesis is \(\boxed{\mathrm{H}_{0} : \sigma \geq 6\%}\)

Step 6 ：Final Answer: The alternative hypothesis is \(\boxed{\mathrm{H}_{1} : \sigma < 6\%}\)