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 3.28?%. Is there sufficient evidence to conclude that the fund has moderate risk at the alpha equals 0.05 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?: ? p sigma mu ? greater than equals less than not equals ? 0.0328. 0.05. The alternative hypothesis is H1?: ? sigma p mu ? equals less than not equals greater than ? 0.0328. 0.05. Calculate the value of the test statistic. chi Subscript 0 Superscript 2equals nothing ?(Round to two decimal places as? needed.) Use technology to determine the? P-value for the test statistic. The? P-value is nothing. ?(Round to three decimal places as? needed.) What is the correct conclusion at the alpha equals 0.05 level of? significance? Since the? P-value is ? less greater than the level of? significance, ? do not reject reject the null hypothesis. There ? is is not sufficient evidence to conclude that the fund has moderate risk at the 0.05 level of significance.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H₀: ? > 5.0

Alternative hypothesis H_A: ? < 5.0

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (X²).

DF = n - 1 = 21 -1

D.F = 20

We use the Chi-Square Distribution Calculator to find P(?² < 8.607) = 0.013

Interpret results. Since the P-value (0.013) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that standard deviation of its monthly rate of return is less than 5%.