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 24 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 2.68​%. Is there sufficient evidence to conclude that the fund has moderate risk at the alpha equals 0.01 level of​ significance? A normal probability plot indicates that the monthly rates of return are normally distributed.

X^2 = ? (Round to three decimal places as needed.)

Use technology to determine the P-value for the test statistic

What is the correct conclusion at the a = 0.01 level of significance?

Answer 1

We have to test the hypothesis that

Whether or not mutual fund has moderate risk?

i.e. Null Hypothesis-

against

Alternative Hypothesis- . ( left-tailed test).

We chi-square test for testing population standard deviation.

The value of test statistic is

Given :

n = 24 , S = 0.0268

The value of chi-square test statistic = 18.3550.

Alpha: Level of significance = 0.01

Degrees of freedom = n-1 = 24-1 = 23.

Since the test is left-tailed and value of test statistic 18.3550.

p-value is obtained by

By using R

> pvalue=pchisq(18.3550,23)
> pvalue
[1] 0.2620412.

p-value = 0.2620

Decision : Since p-value > level of significance alpha, we failed to reject the null hypothesis.

Conclusion : There is insufficient evidence to conclude that the fund has moderate risk at 0.01 level of significance.