Investors not only desire a high return on their money, but they would also like the rate of return to be stable (have a small volatility) from year to year. An investment manager invests with the goal of reducing volatility, measured by the standard deviation, to be less than 4.3. The following data represent the rate of return (in percent) for his mutual fund for the past 12 years. Taking the data as a random sample and assuming that the data follow a normal distribution, is there evidence to support the investor’s claim that his portfolio has a yearly volatility less than 4.3? Use α = 0.1 level of significance.12.8 16.9 9.0 11.4 10.3 5.6 8.6 11.4 9.3 7.7 13.9 5.7Hypotheses:Test statistic. Round to 3 decimals. Critical value(s). Round to 3 decimals.Conclusion in context.

From the provided information, Sample size (n) = 12 Level of significance (α) = 0.1

Answered: Investors not only desire a high return…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 12PPS

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Investors not only desire a high return on their money, but they would also like the rate of return to be stable (have a small volatility) from year to year. An investment manager invests with the goal of reducing volatility, measured by the standard deviation, to be less than 4.3. The following data represent the rate of return (in percent) for his mutual fund for the past 12 years. Taking the data as a random sample and assuming that the data follow a normal distribution, is there evidence to support the investor’s claim that his portfolio has a yearly volatility less than 4.3? Use α = 0.1 level of significance.

12.8 16.9 9.0 11.4 10.3 5.6

8.6 11.4 9.3 7.7 13.9 5.7

Hypotheses:

Test statistic. Round to 3 decimals.

Critical value(s). Round to 3 decimals.

Conclusion in context.

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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