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 25 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 2.11%.Is there sufficient evidence to conclude that the fund has moderate risk at the α=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:
The alternative hypothesis is H1:
Calculate the value of the test statistic.
χ2=[ ] (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 α=0.05 level of significance?
Since the P-value is [ ](Greater , Less) 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.
null hypothesis: Ho: σ = | 3 | |
Alternate hypothesis: Ha: σ < | 3 |
sample size n: = | 25 | |
sample standard deviation s= | 2.1100 |
test statistic X2 =(n-1)s^{2}/ σ^{2}= | 11.872 |
P value = | 0.019 |
Since the P-value is Less than the level ofsignificance ,reject the null hypothesis. There is sufficient evidence to conclude that the fund has moderate risk at the 0.05 level of significance.
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