Project 3 Instructions Based On Larson Farber Sections 52-53
Project 3 Instructionsbased On Larson Farber Sections 52 53go Tot
Based on Larson & Farber: sections 5.2-5.3. Go to the specified website, set the date range to exactly one year ending with the course start date, and download the spreadsheet with the stock's closing values for that period. Use only the closing prices for your analysis. Assume the data is normally distributed and calculate the mean and standard deviation in Excel, then use the methods from sections 5.2 and 5.3 of the textbook to answer the following questions, showing your work or explanations for each answer. Submit a single Excel file with your responses.
Paper For Above instruction
This assignment involves analyzing the closing stock prices of Google over a specified one-year period to understand their statistical properties using principles of normal distribution. The goal is to apply descriptive and inferential statistical procedures to real-world financial data, reinforcing concepts from sections 5.2 and 5.3 of Larson and Farber's textbook.
First, you must access the specified website to retrieve the stock data. Set the date range to be exactly one year ending on the Monday that the course starts. For example, if the course started on January 12, 2015, then your date range should be from January 12, 2014, to January 11, 2015. From the website, download the data as a spreadsheet file, and ensure to focus only on the closing prices, as specified in the instructions.
With the data in hand, use Excel to compute the mean and standard deviation of the closing prices over the period. These are essential parameters for applying normal distribution techniques. The following questions will test your understanding of the properties of normal distributions, probabilities, and statistical uncommonness as defined in your textbook.
Questions and Analysis
1. Probability of closing below the mean
A person who purchased one share of Google stock during the last year faces a certain probability that on any given day, the closing price was below the average for the period. Since the data is assumed normal, the probability that a randomly selected closing price was less than the mean is always 0.5, regardless of specific data. Confirm this by explaining that in a normal distribution, the mean divides the data into equal halves. Therefore, the probability that a stock closes below the mean is 50%.
2. Probability of closing above $400
Calculate the Z-score corresponding to a closing price of $400 using the mean and standard deviation. Then, find the probability that the closing price exceeds $400 using standard normal distribution tables or Excel functions like 'NORM.DIST'. The probability equals 1 minus the cumulative probability up to $400. For example, if Z is calculated as (400 - mean)/SD, then the probability of closing > $400 is 1 - NORM.DIST(400, mean, SD, TRUE).
3. Probability of closing within $45 of the mean
Determine the likelihood that the closing price was within $45 of the mean. This entails calculating the probability that the closing price was between (mean - 45) and (mean + 45). Convert these bounds to Z-scores and find the cumulative probabilities for each. The probability of being within this range is the difference between these two cumulative probabilities: NORM.DIST(mean + 45, mean, SD, TRUE) - NORM.DIST(mean - 45, mean, SD, TRUE).
4. Unusualness of a $362.50 closing price
Using the Z-score formula, assess how many standard deviations $362.50 is from the mean. According to the textbook's definition, a value is considered unusual if it lies more than 2 standard deviations away from the mean (either below or above). If |Z| > 2, then the price is unusual. If it's within 2 SDs, it is not considered unusual.
5. Prices considered statistically unusual
Determine the cutoff prices for unusualness by calculating the bounds at ±2 SDs from the mean: (mean - 2SD) and (mean + 2SD). Prices outside this range are considered statistically unusual. Clearly state these low and high cutoff values based on your data.
6. Quartiles of the data set
Using Excel functions such as 'QUARTILE.EXC' or 'QUARTILE.INC', find Quartile 1 (25th percentile), Quartile 2 (median), and Quartile 3 (75th percentile). These statistical measures provide insight into the spread and central tendency of the dataset, independent of the normality assumption.
7. Validity of the normality assumption
Evaluate whether the closing prices approximate a normal distribution. Construct a histogram with about 10 to 12 classes and observe its shape. A symmetrical, bell-shaped histogram suggests normality. Discuss any skewness, kurtosis, or deviations from the normal pattern. Also, consider alternative tests or plots like Q-Q plots for further validation. Recognize that real data rarely perfectly follow a normal distribution, but a close approximation supports the assumption in your analysis.
This comprehensive analysis combines descriptive statistics, probability computations, and distribution validation to deepen your understanding of stock price behavior through the lens of normal distribution theory. Ensure all calculations, insights, and interpretations are clearly documented in your Excel file, as incomplete or unsupported answers will not receive credit.
References
- Larson, R., & Farber, T. (2014). Elementary Statistics (6th ed.). Pearson Education.
- William, J. (2019). Applied Statistics and Probability for Engineers. Pearson.
- Newbold, P., & Carlson, W. (2014). Statistics for Business and Economics. Pearson.
- Agresti, A., & Franklin, C. (2017). Statistics: The Art and Science of Learning from Data. Pearson.
- Mooney, H. M. (2003). Introductory Statistics. McGraw-Hill Education.
- U.S. Securities and Exchange Commission. (2020). Stock Market Data. https://www.sec.gov
- Yahoo Finance. (2023). Google Stock Data. https://finance.yahoo.com
- Excel Functions Reference. (2023). Microsoft Support. https://support.microsoft.com
- Wilkinson, L. (2012). The Grammar of Graphics. Springer.
- Chatterjee, S., & Hadi, A. (2006). Regression Analysis by Example. Wiley.