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 26 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 4.51%. 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: ▼ pp muμ sigmaσ ▼ equals= not equals≠ less than< greater than> ▼ 0.05. 0.0451. The alternative hypothesis is H1: ▼ muμ pp sigmaσ ▼ equals= greater than> less than< not equals≠ ▼ 0.0451. 0.05. Calculate the value of the test statistic. χ2=nothing (Round to three 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 α=0.05 level of significance? Since the P-value is ▼ less greater than the level of significance, ▼

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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

months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be

4.51%.

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:

▼

muμ

sigmaσ

▼

equals=

not equals≠

less than<

greater than>

▼

0.05.

0.0451.

The alternative hypothesis is

H1:

▼

muμ

sigmaσ

▼

equals=

greater than>

less than<

not equals≠

▼

0.0451.

0.05.

Calculate the value of the test statistic.

χ2=nothing

(Round to three 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

α=0.05

level of significance?

Since the P-value is

▼

less

greater

than the level of significance,

▼

reject

do not reject

the null hypothesis. There

▼

is not

sufficient evidence to conclude that the fund has moderate risk at the

0.05

level of significance.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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