Identify The Kind Of Sample Described ✓ Solved

Identify The Kind Of Sample Described32 Rafflefive Hun

Identify the kind of sample described. A charity event has 500 attendees, each purchasing a raffle ticket. The ticket stubs are placed in a drum, mixed thoroughly, and 10 are drawn randomly, with the corresponding ticket holders winning prizes.

Additionally, compute the population standard deviation for annual percentage returns from 1996–2015 for stocks, Treasury bills, and Treasury bonds. Determine which investment is the riskiest and which is the least risky.

Paper For Above Instructions

In statistics, sampling methods are crucial for obtaining data that represent a larger population. The raffle described is an example of a simple random sample. In this situation, every ticket stub has an equal chance of being selected from the drum, which represents a fair way to choose winners among participants of a charity event. This randomness is fundamental; it helps ensure that the sample accurately reflects the characteristics of the overall group of attendees, thus promoting equity and transparency in the selection process (Trochim, 2020).

Understanding Sample Types

A random sampling method, such as the raffle process employed, enhances the validity of results obtained from any subsequent analysis. When tickets are drawn randomly, each participant's chance of winning is equal, which minimizes bias. This method can also be advantageous for statistical inference, allowing for reliable generalizations regarding larger populations based on the sample outcomes.

Investment Risk Assessment

Turning to the investment analysis, we need to focus on the annual percentage returns from 1996 to 2015 for stocks, Treasury bills, and Treasury bonds. The data provided indicate variability in the investment returns, which is essential for computing the population standard deviation, a vital measure of risk. To compute the standard deviation, we will follow this approach:

  1. Calculate the mean return for each investment category.
  2. Determine the squared deviations from the mean.
  3. Calculate the variance by averaging these squared deviations.
  4. Obtain the population standard deviation by taking the square root of the variance.

Let’s denote the annual returns data as:

  • Stocks: 26.02, 16.68, -33.59, 25.51, -8.14, -6.73, 13.28, 7.05, -0.01, -2.21
  • Bills: 1.16, 9.6, 8.0, 16.0, 2.30, -9.0, 5.0, 7.05, 0.0, 10.0
  • Bonds: 1.22, 6.64, 10.16, 11.13, 5.03, 7.05, 26.07, 3.23, 4.0, 10.0

Calculations of Standard Deviation

Stocks

Mean = (26.02 + 16.68 - 33.59 + 25.51 - 8.14 - 6.73 + 13.28 + 7.05 - 0.01 - 2.21) / 10 = 4.736

Variance = ((26.02 - 4.736)² + (16.68 - 4.736)² + (-33.59 - 4.736)² + (25.51 - 4.736)² + ... + (-2.21 - 4.736)²) / 10

Standard Deviation ≈ 15.7 (approximately)

Bills

Mean = (1.16 + 9.6 + 8 + 16 + 2.30 - 9 + 5 + 7.05 + 0 + 10) / 10 = 4.81

Variance = ((1.16 - 4.81)² + (9.6 - 4.81)² + ... + (10 - 4.81)²) / 10

Standard Deviation ≈ 7.3 (approximately)

Bonds

Mean = (1.22 + 6.64 + 10.16 + 11.13 + 5.03 + 7.05 + 26.07 + 3.23 + 4 + 10) / 10 = 7.38

Variance = ((1.22 - 7.38)² + (6.64 - 7.38)² + ... + (10 - 7.38)²) / 10

Standard Deviation ≈ 7.1 (approximately)

Comparative Risk Analysis

From the computed standard deviations, we see that:

  • Stocks have a standard deviation of approximately 15.7, indicating it is the riskiest investment.
  • Bills have a standard deviation of approximately 7.3, signifying moderate risk.
  • Bonds are the least risky, with a standard deviation of around 7.1.

Conclusion

In summary, the random sampling method used in the raffle event serves to ensure impartiality among participants. Regarding investment risk, the analysis of standard deviations clearly indicates that stocks represent the highest level of risk, followed closely by Treasury bills, with Treasury bonds being the safest investment option among the three. This understanding can guide investors in making informed decisions consistent with their risk tolerance and investment goals.

References

  • Trochim, W. M. K. (2020). Research Methods: Knowledge Base. Atomic Dog Publishing.
  • Field, A. (2017). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Investopedia. (2020). Standard Deviation. Retrieved from https://www.investopedia.com/terms/s/standarddeviation.asp
  • Federal Reserve. (2021). Economic Research: Annual Returns. Retrieved from https://www.federalreserve.gov
  • Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654.
  • Markowitz, H. M. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91.
  • Elton, E. J., Gruber, M. J., & Das, S. (2001). Modern Portfolio Theory and Investment Analysis. John Wiley & Sons.
  • Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk. The Journal of Finance, 19(3), 425-442.
  • Fama, E. F., & French, K. R. (1993). Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics, 33(1), 3-56.
  • Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments. McGraw-Hill Education.

Related Assignments