### Understanding P-Value in Hypothesis Testing**Problem Statement:**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 2.63%. 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.**Step-by-Step Solution:**1. **Null Hypothesis (H0):** - The standard deviation of the mutual fund's rate of return is equal to or greater than 4%. - $\sigma \geq 4\%$2. **Alternative Hypothesis (H1):** - The standard deviation of the mutual fund's rate of return is less than 4%. - $\sigma < 4\%$3. **Given Data:** - Sample size, $n = 21$ - Sample standard deviation, $s = 2.63\%$ - Population standard deviation threshold, $\sigma = 4\%$ - Significance level, $\alpha = 0.05$4. **Use technology to determine the P-value for the test statistic.** You'll need to use a statistical software or calculator to determine the precise P-value. The general process involves using the chi-square distribution because it is based on the sample standard deviation and the sample size. 5. **P-Value Calculation:** The formula for the test statistic using chi-square distribution is: \[ \chi^2 = \frac{(n-1)s^2}{\sigma^2} \] Substitute the given values: \[ \chi^2 = \frac{(21-1)(2.63)^2}{(4)^2} \] \[ \chi^2 = \frac{20 \times 6.9169}{16} \] \[ \chi^2 = \frac{138.338}{16} \] \[ \chi^2 \approx 8.646 \] Next, use a chi-square distribution table or technology to

Sample size n=21 Population standard deviation σ=0.04 Sample standard deviation s=0.0263…

Answered: Suppose a mutual fund qualifies as…

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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