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 \(\boxed{\mathrm{H}_{1} : \sigma < 6\%}\)