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AP STATISTICS PROJECT #3 The Product Proportion Comparison Project You have just been hired as marketing researchers within a particular company. Your task is to prove or disprove the company’s current claim concerning their product by comparing it to TWO other similar products through a survey or an experiment. Your result will be written up in a report to the CEO along with all supporting data. For example: PEPSI ‘s current position is that a higher proportion of the population drinks PEPSI than COKE or Dr. Pepper. You would conduct an experiment/survey, collect the data, and compute the sample proportions. You would then conduct a Significance Test to determine whether there actually is a difference in proportions. For example: CHIPS A’HOY, the chocolate chip cookie company, has a current position that there are a higher proportion of chips in their cookies than NESTLE . You would carry out an experiment that would examine the proportion of cookies that have an average amount of chips, calculate the proportions, and then conduct a Significance Test to determine whether there actually is a difference in proportions. For example: ATT advertises that there are a significantly different proportion of people using ATT than MCI. You would conduct an experiment/survey, collect the data, and compute the sample proportions. You would then conduct a Significance Test to determine whether there actually is a difference in proportions. PART I - ONE – PROPORTION COMPARISON 1. Choose a particular company that sells, markets, and advertises a certain product or idea. The product or idea must have a marketing or advertisement claim. In your report include detailed background information about this company. Give a brief history of the company’s product or idea that you are investigating. 2. DESIGN a Survey or an Experiment to examine and compare the company’s product or idea with TWO other companies of similar products. You will survey or use an experiment to determine which one of the three products/concepts the respondent prefers best. Your sample must be (but not limited to) a sample size of 45. Describe how you carried out this survey or experiment? How was randomization incorporated in your design? This description should be very detailed. How did you avoid many of the cautions associated with experimental design or sampling? Could there be any sampling bias? Are there any confounding variables? How did you address them? 3. The experiment should establish three separate counts, the number of respondents that respond favorable to each of the three products. a = the number of respondents in favor of your product, b = the number of respondents in favor of your alternative product #1, and c = the number of respondents in favor of your alternative product #2. Create a histogram representing the percent of respondents in favor of each or three products. Probability 4. Showing all work, calculate the probability that more than half of the respondents favored your product. 5. Showing all work, calculate the probability that less than a third of the respondents favored your alternative product #1. Confidence Intervals 6. Showing all steps of a Confidence interval, calculate the true proportion of the population that favors your product. (Be sure to check the assumptions and answer in context.) 7. Showing all steps of a Confidence interval, calculate the true proportion of the population that favors alternative product #1. (Be sure to check the assumptions and answer in context.) 8. Showing all steps of a Confidence interval, calculate the true proportion of the population that favors alternative product #2. (Be sure to check the assumptions and answer in context.) Hypothesis Tests 9. It has been claim that more than 50% of the population favors your product. Use your collected data and a one proportion hypothesis test to determine if there is any evident disregarding the claim. State your Parameters, Hypothesis, Test Name AND Formula, state the results in context, and test the assumptions. 10. Conduct a TWO separate Two-Proportion hypothesis tests to determine if YOUR product is preferred more than the first or second alternative product. In the first hypothesis test use the data collected for your product and the first alternative. In the second hypothesis test use the data collected for your product and the second alternative. For both tests, is there significant evidence that your product is more widely favored over the alternative? State your Parameters, Hypothesis, Test Name AND Formula, state the results, and test the assumptions. THE REPORT You must prepare a letter to the CEO of your company, which is ME (Mr. Lance A. Belin). In this report, comment about favorability of your product. This report must be a 100% typed report with at least 200 words, have a cover page, have a very creative title, be very detailed, include a statement of what you expected before the experiment, how you collected the sample, and include a description of the results. The report should include support for your conclusion with p-hats, graphs, hypotheses, assumptions, z-scores, p-values, and conclusions in Laymen’s terms. Finally, based on the results of all inferences, how should the company change their current marketing and advertising campaigns?