Question

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 22 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 4.22%. Is there sufficient evidence to conclude that the fund has moderate risk at the α=0.01 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 H0 :

The alternative hypothesis is H1 :

Answer 1

Here we need to test if the standard deviation is less than 6% (0.06)

So alternate hypothesis would be

Standard deviation(σ)

And as we know that null hypothesis is always the opposite of the alternate hypothesis,

So null would be

σ >= 0.06

Null hypothesis Ho : σ >= 0.06

Alternate Ha : σ