Complete the following AND SHOW ALL WORK: 1. In paragraph form, describe your topic. You may choose any topic you wish as long as it involves quantitative data (numbers) of some kind. Identify the relevant population relating to your topic. Next, obtain data in order to address your question of interest. Collect a sample related to your question of interest where the sample size (n) is 30 or more by conducting a survey. Remember, the data must be quantitative as the term is defined in the text (for example, the ages of best actresses in the text), so for whatever survey question you ask, the answer must be a number. In paragraph form, describe how you obtained your data, including the phrasing of the question you asked and how you conducted your poll (e.g. asked friends, family, coworkers; went to a mall, chat rooms, etc.). If you are unsure as to whether or not your data is quantitative, please contact me for help. 2. For your quantitative data a. Provide a list of your original data. This should be a list of at least 30 numbers. b. Create a frequency distribution table using at least 5 classes. Show the class limits (including the calculation to get class width, etc.), class frequencies, relative frequencies, and cumulative frequencies. c. Create a histogram using the class frequencies from part (b) (see Chapter 2-3). d. Calculate the mean, median, and mode using the methods described in Chapter 3-2. e. Calculate the standard deviation and the variance from the original data. Use either Formula 3-4 or 3-5 for the standard deviation calculation. f. Calculate the 5-number summary. Show ALL your work! 3. Assume that the data is bell-shaped. Use the mean and standard deviation to find the limits for 68%, 95%, and 99.7% of the data. (Hint: Empirical Rule) Show ALL your work! 4. Propose a hypothesis about the proportion AND mean of your quantitative data. a. Your proportion hypothesis must contain only one number. For example, looking at the Best Actress Ages example in the text, “at least 25% of best actresses are in her 30s”, “more than 30% are older than 30”, or “15% are 35” are acceptable, “between 10% and 30% are 35” is not. i. Calculate the proportion (to which you refer with your proportion hypothesis) of your data. For example, x% of best actresses were in her 30s. ii. Calculate the 95% Confidence Interval for the proportion. b. Your mean hypothesis must also contain only one number. For example “the average is at most 30 years old”, “the average is under 25”, or “the average is not 40” are acceptable, “the average is between 15 and 40” is not. i. Using the sample mean and standard deviation (from #2 above, also see Chapter 3), calculate the 95% Confidence Interval for the population mean (see Chapter 7-4). Show ALL your work!
5. You will test both hypotheses using the data you have collected. a. Use your survey results and the p-value method to test the proportion hypothesis you proposed. Show work for all steps including the formulas you use. Use α = 0.05. b. Use your survey results and the traditional method to test the mean hypothesis you proposed. Show work for all steps including the formulas you use. Use α = 0.05 (see Chapter 8-5). 6. In paragraph form, describe what you have found and write your conclusions based on your sample and the analyses you have performed. Your report should be typed and neatly organized. All the requirements must be in ONE document (i.e. do not send along 10 different files, each with bits of the report). You may perform your analysis using a computer, or you may do it by hand. In either case, ALL WORK MUST BE SHOWN, and it must be neat and organized. Sharing data or work between groups is NOT allowed. Your report must be turned in on the due date listed at the top of this page. Late reports will be penalized 15 points initially, then an additional 10 points each day beyond the due date.