Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 4%. 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 2.71%. 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: σ or μ or p and less than or not equal or greater than or equals 2.7. The alternative hypothesis is H1: μ or p or σ , greater than or less than or not equals or equals 2.7. Calculate the value of the test statistic. X2 = _ (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 ?=0.10 level of? significance? Since the P-value is than the level of? significance, _ the null hypothesis. There _ sufficient evidence to conclude that the standard deviation of heights of? major-league baseball players is less for?major-league baseball players at the 0.10 level of significance.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 4%. 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 2.71%. 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: σ or μ or p and less than or not equal or greater than or equals 2.7.

The alternative hypothesis is H1: μ or p or σ , greater than or less than or not equals or equals 2.7.

Calculate the value of the test statistic.

X2 = _____ (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 ?=0.10 level of? significance?

Since the P-value is ____ than the level of? significance, _______ the null hypothesis. There _____ sufficient evidence to conclude that the standard deviation of heights of? major-league baseball players is less for?major-league baseball players at the 0.10 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.

Expert Solution

Step 1

The hypotheses for the test are given below:

Null hypothesis:

H₀: σ=0.04.

Alternative hypothesis:

H₁: σ<0.04.

The sample standard deviation is 0.0271.

Sample size, n is 21.

The test statistic for Chi-square test is calculated as given below.

$\begin{matrix} χ^{2} = \frac{(n - 1) s^{2}}{σ^{2}} \\ = \frac{(21 - 1) {(0.0271)}^{2}}{{(0.04)}^{2}} \\ = 9.180 \end{matrix}$

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