Stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The table below lists the annualized percentage return on investment (as compared to the Standard & Poor’s 500 Index) for 13 randomly selected stock screeners provided by the American Association of Individual Investors (AAII). 9.0 -0.1 -1.6 14.6 16.0 7.7 19.9 9.8 3.2 24.8 17.6 10.7 9.1 The summary statistics are: a. Do you think the data has an approximately normal distribution, according to the analysis below? Answer: YES NO Note: The Null Hypothesis for the Shapiro-Wilk test is “The data is Normal” b. Find a 90% confidence interval for the average annualized percentage return on investment of all stock screeners provided by AAII. Answer: (7.01 , 14.63), n =13, sample mean = 10.82, sample sd= 7.71, t c. The AAII reports that the average annualized percentage return on investment of all stock screeners is expected to be µ = 8.5 this year. Do you agree with this claim based on the collected data? Use a two-tailed alternative hypothesis, with α = 0.10. Answer: Fill in the expressions below Ho: Ha: CV = RR = Test statistics = P-value = Conclusion: Keep Ho Reject Ho (extra credit) e) Obtain a 90% confidence interval for σ2, and get a conclusion about Ho: σ2 = 65 Answer: Conclusion from this CI: Keep Ho: σ2 = 65 Reject Ho By the way, what is Ha in this case?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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7.- Stock screeners are automated tools used by investment companies to help clients select a portfolio

of stocks to invest in. The table below lists the annualized percentage return on investment (as compared to the Standard & Poor’s 500 Index) for 13 randomly selected stock screeners provided by the American Association of Individual Investors (AAII).

9.0 -0.1 -1.6 14.6 16.0 7.7 19.9 9.8 3.2 24.8 17.6 10.7 9.1 The summary statistics are:

a. Do you think the data has an approximately normal distribution, according to the analysis below?

Answer: YES NO

Note: The Null Hypothesis for the Shapiro-Wilk test is “The data is Normal”

b. Find a 90% confidence interval for the average annualized percentage return on investment of all stock screeners provided by AAII.

Answer: (7.01 , 14.63), n =13, sample mean = 10.82, sample sd= 7.71, t

c. The AAII reports that the average annualized percentage return on investment of all stock screeners is expected to be µ = 8.5 this year. Do you agree with this claim based on the collected data? Use a two-tailed alternative hypothesis, with α = 0.10.

Answer: Fill in the expressions below

H_o: H_a: CV = RR = Test statistics = P-value =

Conclusion: Keep H_o Reject H_o

(extra credit) e) Obtain a 90% confidence interval for σ², and get a conclusion about H_o: σ² = 65

Answer:

Conclusion from this CI: Keep H_o: σ² = 65 Reject H_o

By the way, what is H_a in this case?

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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