Question

Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 5​%. A​ mutual-fund rating agency randomly selects 21 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 3.42​%. 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.

Answer 1

Claim: The standard deviation of the monthly rate of return is less than 5.

Sample size = n = 21

Sample standard deviation = s = 3.42

The null and alternative hypothesis is

Test statistic is

Degrees of freedom = n - 1 = 21 - 1= 20

Level of significance = 0.01

Critical value = 37.566

( From chi-square table)

Test statistic < critical value we fail to reject null hypothesis.

Conclusion: The fund has not moderate risk.