Project Instructions Based On Larson Farber Sections 52-53 N

Project3instructionsbasedon Larson Farber Sections 5253note That

Complete this project on your own, using the provided website to download stock closing prices for exactly one year ending on the Monday that the course started. Use the spreadsheet's close values, assume a normal distribution, and calculate the mean and standard deviation. Use Excel to find these values and answer the questions based on methods from sections 5.2–5.3 of your textbook.

Submit a file containing your dataset and responses, with explanations or work shown for each answer. Answers without supporting work will not receive credit.

Paper For Above instruction

In this project, the primary goal was to analyze the stock closing prices of Google over a period of exactly one year, applying statistical methods rooted in the assumption that the data follow a normal distribution. This involved the systematic calculation of key statistical measures, understanding probabilities associated with the normal distribution, and evaluating the normality of the data.

First, data collection was conducted by downloading the stock closing prices from a specified website, ensuring that the date range was precisely one year ending on the course start date. The dataset comprised daily closing prices, which served as the foundation for all subsequent statistical analysis. The dataset was then imported into Excel for analysis.

Calculating the mean and standard deviation was the initial step. The mean provides the average closing price over the period, while the standard deviation measures the typical variation from this average. These calculations are crucial for understanding the central tendency and dispersion of the data set and are essential for computing probabilities related to the normal distribution.

Once the descriptive statistics were established, probability questions based on the normal distribution were addressed. For instance, the probability that on a randomly selected day, the stock price was less than the mean was explored. Since under normality, the probability of a value being less than the mean is 0.5, this served as a validation checkpoint. Similarly, the probability of the stock closing at more than $600 was calculated using the standard normal table and z-scores. The z-scores were derived by subtracting the mean from the value of interest and dividing by the standard deviation.

Another key analysis involved determining the probability that the stock's closing price fell within $45 of the mean, which required calculating the z-scores for the bounds (mean ± $45) and then finding the corresponding probabilities. Additionally, the analysis discussed whether a closing price of $450 was unusual. Using the textbook's criteria, any value more than two standard deviations away from the mean was classified as unusual. This involved calculating the z-score for $450 and comparing it with the threshold values.

To find the price bounds for statistical un usuality, the analysis inverted the process: identifying the lower and upper bounds that are two standard deviations below and above the mean, respectively. Stocks closing outside these bounds are deemed statistically unusual.

Using Excel, quartiles were calculated for the dataset to understand its distribution better. Quartiles help segment the data into four parts, providing insights into the data's spread and skewness. Q1 (the first quartile), Q2 (the median), and Q3 (the third quartile) were determined using Excel's built-in functions.

Assessment of the normality assumption was critical. The normality of the stock prices was evaluated by constructing a histogram with approximately 10-12 bins. The shape of this histogram was visually inspected to see if it resembled the bell curve characteristic of a normal distribution. The properties of symmetry and the distribution of data around the mean were analyzed to determine if the assumption was valid.

Finally, additional points were awarded for meticulousness, including correct data range, accurate calculations of mean and standard deviation, appropriate use of formulas, and correct interpretative statements. This comprehensive analysis enhances understanding of stock price behavior and the applicability of the normal distribution model.

References

• Larson, R., & Farber, M. (2014). Elementary Statistics (5th ed.). Pearson.
• DeGroot, M. H., & Schervish, M. J. (2012). Probability and Statistics (4th ed.). Pearson.
• Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics (8th ed.). Pearson.
• Everitt, B. S., & Skrondal, A. (2010). The Cambridge Dictionary of Statistics (2nd ed.). Cambridge University Press.
• Wasserman, L. (2004). All of Statistics: A Concise Course in Statistical Inference. Springer.
• Gujarati, D. N., & Porter, D. C. (2009). Basic Econometrics (5th ed.). McGraw-Hill.
• Hogg, R. V., & Tanis, E. A. (2006). Probability and Statistical Inference (8th ed.). Pearson.
• McClave, J. T., & Sincich, T. (2012). Statistics (11th ed.). Pearson.
• Sullivan, M., & Wicks, E. (2013). Business Statistics: A First Course. Pearson.
• Anderson, D. R., Sweeney, D. J., & William, M. T. (2015). Statistics for Business and Economics (12th ed.). Cengage Learning.