Comparing Populations Using Statistical Inference Resources
Comparing Populations Using Statistical Inference Resources Comparing Populations Using Statistical Inference
For this assignment, you will practice applying statistical inference to business decision scenarios involving stock data analysis from Yahoo Finance. The exercise includes three practical scenarios focusing on hypothesis testing of stock prices, specifically examining mean daily closing volumes and prices over different periods and frequencies. You are required to download the relevant data, formulate hypotheses, identify and conduct the appropriate statistical tests, interpret the results, and write concise explanations in layman's terms. Additionally, you must prepare a Word document compiling your answers and visualizations, and submit the raw data as a CSV file for instructor verification.
Paper For Above instruction
In the realm of business and financial decision-making, statistical inference provides critical tools for analyzing stock market data to discern meaningful patterns and make informed predictions. This assignment guides students through practical applications of hypothesis testing using historical stock data from Yahoo Finance, focusing on three distinct scenarios that involve comparing means across time and frequency. Through these exercises, students learn to formulate hypotheses, select appropriate tests, interpret statistical results, and communicate findings clearly.
Scenario 1: Comparing Daily Closing Volumes for Two Stocks
The first scenario involves analyzing whether there is a statistically significant difference in the mean daily closing volume between two stocks over the past five years. Students are instructed to select a stock starting with the first letter of their first name, download five years of daily data, and match this data with another stock starting with the same first letter to control for market influences. The null hypothesis (H₀) posits that there is no difference in the mean daily closing volumes between the two stocks, while the alternative hypothesis (H₁) suggests a difference exists:
H₀: μ₁ = μ₂ (The mean daily closing volumes are equal)
H₁: μ₁ ≠ μ₂ (The mean daily closing volumes are not equal)
The appropriate statistical test for this comparison is the paired samples t-test, as the data are matched pairs based on the date. The test compares the mean differences in closing volumes for each paired date, accounting for variability across days. Conducting this test involves calculating the test statistic and p-value, then interpreting whether the p-value is less than the significance level of 0.05 to determine if the null hypothesis can be rejected. A rejection indicates a significant difference between the two stocks' volumes; otherwise, the data do not support such a difference.
In layman’s terms, if the p-value is less than 0.05, we can confidently say that the mean daily closing volume of the two stocks is different; if it is greater, we have no evidence to suggest a difference. If the significance level was set at 0.01 instead, our criteria for confidence would be more stringent, requiring even stronger evidence to reject the null hypothesis, making it less likely to find differences significant.
Scenario 2: Comparing Mean Prices Over Two Time Periods
The second scenario analyzes whether the mean daily adjusted closing price over the last three years has increased compared to the first two years for a stock starting with the last letter of the student's last name. After downloading the data, students formulate hypotheses: the null hypothesis claims no change in the mean prices, while the alternative posits an increase:
H₀: μ₁ = μ₂ (The mean price over the first two years equals that of the last three years)
H₁: μ₂ > μ₁ (The mean price over the last three years is higher than the first two)
The appropriate test here is a one-sample t-test comparing the second period's mean to the first period’s mean (or a two-sample t-test if considering independent samples, assuming data independence). The analysis involves calculating means, standard deviations, and the test statistic, then comparing the resulting p-value to 0.05. A p-value less than this threshold indicates a statistically significant increase in mean prices over time, allowing rejection of the null hypothesis.
Communicating this in layman’s terms, if the p-value is below 0.05, there is strong evidence that the stock’s average price has increased in the last three years compared to the previous two. Should the significance level be set at 0.01, only a very low p-value would justify rejecting the null hypothesis, indicating a more rigorous threshold for confirming an increase.
Scenario 3: Monthly Differences in Adjusted Closing Prices Over Five Years
The third scenario explores whether the monthly mean adjusted closing price for a specified stock differs over the five-year period. Students download five years of monthly data, changing the frequency to monthly, then perform an ANOVA or equivalent hypothesis test to evaluate differences across months. The null hypothesis states there is no difference in the mean monthly prices, whereas the alternative suggests variations across months:
H₀: μ₁ = μ₂ = ... = μ₁₂ (All monthly means are equal)
H₁: At least one monthly mean differs
The suitable test for this scenario is one-way ANOVA, which compares the means across multiple groups (months). The analysis involves calculating group means, variances, and the ANOVA F-statistic, with a p-value indicating whether at least one month’s mean differs significantly from others. Rejecting H₀ at the 0.05 significance level implies that the stock’s price varies across months. Accepting H₀ suggests stability in monthly prices over the five-year period.
In simple terms, if the p-value is below 0.05, we conclude some months have higher or lower averages than others, indicating seasonal or other periodic effects. If we set alpha at 0.01, only very strong evidence will lead us to conclude that the monthly prices are significantly different, emphasizing more conservative criteria for significance.
Conclusion
This assignment integrates the principles of statistical hypothesis testing with real-world stock data analysis, enabling students to develop skills in data collection, hypothesis formulation, test selection, and interpretation. By engaging with these scenarios, students gain insights into financial data behavior and acquire practical experience in applying statistical methods to business decisions. Communication of results in layman's terms is emphasized to ensure clarity and applicability beyond statistical jargon, fostering better understanding of the importance and implications of statistical inference in finance.
References
- Agresti, A., & Finlay, B. (2009). Statistical Methods for the Social Sciences (4th ed.). Pearson.
- Glen, S. (2010). Hypothesis testing. Statistics How To. https://www.statisticshowto.com/hypothesis-test/
- Field, A. (2013). Discovering Statistics Using SPSS (4th ed.). Sage Publications.
- Hogg, R. V., & Tanis, E. A. (2015). Probability and Statistical Inference (9th ed.). Pearson.
- Newbold, P., Carlson, W. L., & Thorne, B. M. (2013). Statistics for Business and Economics (8th ed.). Pearson.
- Schwab, J. J., & Clemens, M. (2014). Financial Market Graphs and Data. University of Chicago Press.
- Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press.
- Salkind, N. J. (2010). Statistics for People Who (Think They) Hate Statistics (4th ed.). Sage Publications.
- Stock, J. H., & Watson, M. W. (2015). Introduction to Econometrics (3rd ed.). Pearson.
- Yoo, B. K., & Jun, K. S. (2019). Practical Applications of Hypothesis Testing in Financial Data. Journal of Financial Analysis, 73(2), 122-137.