Question

Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 3​%. A​ mutual-fund rating agency randomly selects 29 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 1.96​%. Is there sufficient evidence to conclude that the fund has moderate risk at the alpha equals 0.10 level of​ significance? A normal probability plot indicates that the monthly rates of return are normally distributed.

Answer 1

Here we want to test "Whether the mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 3​% ?"

Let's write null hypothesis ( H₀ ) and the alternative hypothesis ( H₁) from the above claim is as followes:

Let's use minitab:

Step 1) Click on Stat>>>Basic Statistics >>1 variance...

Data : Select "sample standard deviation"

Sample size: n = 29

Sample standard deviation: 1.96

Then select "Perform hypothesis test"

Look the following image:

Step 2) Click on Option

Confidence level = 90

Alternative: less than

Then click on OK

Again Click on OK

So we get the following output:

From the above output, we get

p- value = 0.004

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value =0.004 which is less than 0.10 so we used first rule.

That is we reject null hypothesis

Conclusion: At 10% level of significance there are sufficient evidence to conclude that the fund has moderate risk.