Question

Question Help 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 23 months and determines the rate of retun for a certain fund. The standard deviation of the rate of return is computed to be 4.66 %. Is there sufficient evidence to conclude that the fund has moderate risk at the a 0.10 level of significance? Anormal probability plot indicates that the monthly rates of retum are normally distributed What are the correct hypotheses for this test? The nul hypothesis is H The altenative hypothesis is H, Calculate the value of the test statistic. 2(Round to three decimal places as needed) Use technology to determine the P-value for the test statistic The P-value is (Round to three decimal places as needed) What is the correct conclusion at the a 0.10 level of significance? sufficient evidence to conclude that the fund has moderate risk at the 0. the null hypothesis. There than the level of significance Since the P-value is level of significance

Answer 1

Answer

We have to test whether the standard deviation is less than 5% or not. It is a left tailed hypothesis test.

$H_o: \sigma = 0.05 \\ H_1: \sigma < 0.05$

Given that is

sample standard deviation s = 0.0466

Population standard deviation $\sigma = 0.05$

sample size n = 23

test statistic

$\chi^2 = ((n-1)*s^2)/\sigma^2 \\ =((23-1)*0.0466^2)/0.05^2 \\ = 0.0478/0.0025 \\ = 19.110$

p value = CHIDIST(x,n-1)

set x = 19.110 and n = 23

we get, p value = CHIDIST(19.110,23-1) = 0.639

p value is greater than 0.10, i.e. 0.639 > 0.10, failed to reject the null hypothesis

Since p value is more than level of significance, Failed to reject the null hypothesis. There is not sufficient evidence to conclude that the fund has moderate risk.