Question

# Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly...

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= 2.11
 test statistic X2 =(n-1)s2/ σ2= 11.872
 P value = 0.019

Since the​ P-value is  Less  than the level of​significance ,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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