CASE STUDY Feeling Lucky? Well, Are You?
In fiscal year (FY) 2013–2014 (July 2013–June 2014), the Florida Lottery generated $5.37 billion in total sales. Over that period, the state spent $37.5 million on advertising to promote its various games. Rand Advertising is interested in gaining access to this lucrative market. You are assigned the task of preparing a report on the lottery sales structure for three of Florida’s online (nonscratch-off ticket) games: Fantasy 5, Lucky Money, and Lotto. Your findings will become part of a proposal by Rand to the Florida Lottery.
In Fantasy 5, a player picks five numbers from 1 to 36, at $1 per play. Drawings are held seven days a week. If there is no jackpot winner for a drawing, the money allocated for the top prize rolls down to the next prize tier (4 of 5).
The Lucky Money game costs $1 per ticket. Players pick four numbers from 1 to 47 and one Lucky Money number from 1 to 22. Drawings are held on Tuesdays and Fridays. If there is no jackpot winner for a drawing, the money allocated for the top prize rolls over to the next drawing, adding to the total of the next jackpot. The prize structures for both games is as shown.
Prize Structure for Florida’s Fantasy 5 Game | ||
Match | Estimated Prize Amount per Winner | Probability |
5 of 5 | $200,000 |
|
4 of 5 | $100 |
|
3 of 5 | $10 |
|
2 of 5 | Free ticket |
|
Prize Structure for Florida’s Lucky Money Game | ||
Match | Estimated Prize Amount per Winner | Probability |
4 of 4 + Lucky Ball | $500,000 |
|
4 of 4 | $1044 |
|
3 of 4 + Lucky Ball | $292 |
|
3 of 4 | $71.50 |
|
2 of 4 + Lucky Ball | $20 |
|
1 of 4 + Lucky Ball | $2.50 |
|
2 of 4 | $2 |
|
0 of 4 + Lucky Ball | Free ticket |
|
In Lotto, players pick six numbers from 1 to 53, at $1 per play. Drawings are held on Wednesdays and Saturdays. If there is no jackpot winner, the top prize is rolled over to the next drawing. It is difficult to win the Lotto jackpot, so there are numerous jackpot rollovers. Rollovers make it difficult to determine an estimated prize payout per winner. However, the odds structure is shown in the table below.
Match | Probability |
6 of 6 |
|
5 of 6 |
|
4 of 6 |
|
3 of 6 |
|
To conduct your study, you have obtained the sales figures for each of the three games by district sales office for one week. These data are as follows:
Are the numbers of tickets sold for each lottery game and sales district independent? Construct a bar graph that represents the conditional distribution of game by sales district. Does this graphical evidence support your conclusion regarding the relationship between the type of game and the sales district? Explain.
Additionally, you are interested in the daily sales structure for the various districts. The table on the following page represent the numbers of tickets sold each day for a randomly selected week for the three games in District 1.
Does the evidence suggest that the proportion of Fantasy 5 sales is the same for each day of the week? Perform a similar test for Lucky Money and Lotto.
Write a report detailing your assumptions, analyses, findings, and conclusions.
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Fundamentals of Statistics (5th Edition)
- I need some help with sections D, E, and F pleasearrow_forwardSchool Newsletter The school photocopying budget continues to increase and the office manager is looking for ways to cut costs. In the most recent publication of the school newsletter, they invited school families to complete a survey indicating how they currently accessed the school newsletter. The options included as possible responses were: • Printed copy sent home each Thursday • Website link sent through via email or • The school app on their smart phone The survey was optional and allowed participants to select more than one response. If participants completed the survey, they were required to select at least one response, but could select more if applicable. The school has 412 students enrolled from 228 families. The Venn diagram below shows the survey results. Printed II. 34 families did not respond to the survey. 41 1. 102 families indicated they view the newsletter via email link and/or the school app, but not a printed copy. III. 21 families' responses indicated that they…arrow_forwardYou may need to use the appropriate technology to answer this question. The Wall Street Journal's Shareholder Scoreboard tracks the performance of 1,000 major U.S. companies. The performance of each company is rated based on the annual total return, including stock price changes and the re investment of dividends. Ratings are assigned by dividing all 1,000 companies into five groups from A (top 20%), B (next 20%), to E (bottom 20%). Shown here are the one- year ratings for a sample of 60 of the largest companies. A C 6 8 14 20 12 Do the largest companies differ in performance from the performance of the 1,000 companies in the Shareholder Scoreboard? Use a = 0.05. State the null and alternative hypotheses. Ho: The proportions of the largest companies compared to the 1,000 companies are the same for at least one of the five groups. H: The proportions of the largest companies compared to the 1,000 companies are different for all five groups. Ho: The proportions of the largest companies…arrow_forward
- Can someone help me solve this please?arrow_forwardAn insurance company offers four different deductible levels-none, low, medium, and high-for its homeowner's policyholders and three different levels-low, medium, and high-for its automobile policyholders. The accompanying table gives proportions for the various categories of policyholders who have both types of insurance. For example, the proportion of individuals with both low homeowner's deductible and low auto deductible is 0.07 (7% of all such individuals). Homeowner's H N L M 0.04 0.07 0.05 0.01 0.07 0.08 0.20 0.13 0.02 0.03 0.15 0.15 Auto L M H Suppose an individual having both types of policies is randomly selected. (a) What is the probability that the individual has a medium auto deductible and a high homeowner's deductible? 0.13 (b) What is the probability that the individual has a low auto deductible? A low homeowner's deductible? auto deductible 0.17 homeowner's deductible (c) What is the probability that the individual is in the same category for both auto and homeowner's…arrow_forwardAn insurance company offers four different deductible levels-none, low, medium, and high-for its homeowner's policyholders and three different levels-low, medium, and high-for its automobile policyholders. The accompanying table gives proportions for the various categories of policyholders who have both types of insurance. For example, the proportion of individuals with both low homeowner's deductible and low auto deductible is 0.07 (7% of all such individuals). Homeowner's Auto N L M H 0.04 0.07 0.05 0.01 M 0.07 0.11 0.20 0.10 H 0.02 0.03 0.15 0.15 Suppose an individual having both types of policies is randomly selected. (a) What is the probability that the individual has a medium auto deductible and a high homeowner's deductible? (b) What is the probability that the individual has a low auto deductible? A low homeowner's deductible? auto deductible homeowner's deductible (c) What is the probability that the individual is in the same category for both auto and homeowner's deductibles?…arrow_forward
- An insurance company offers four different deductible levels-none, low, medium, and high-for its homeowner's policyholders and three different levels-low, medium, and high-for its automobile policyholders. The accompanying table gives proportions for the various categories of policyholders who have both types of insurance. For example, the proportion of individuals with both low homeowner's deductible and low auto deductible is 0.07 (7% of all such individuals). Auto L M H Homeowner's NLMH Suppose an individual having both types of policies is randomly selected. (a) What is the probability that the individual has a medium auto deductible and a high homeowner's deductible? 0.04 0.07 0.05 0.02 0.07 0.09 0.20 0.11 0.02 0.03 0.15 0.15 (b) What is the probability that the individual has a low auto deductible? A low homeowner's deductible? auto deductible homeowner's deductible (c) What is the probability that the individual is in the same category for both auto and homeowner's deductibles?…arrow_forwardPart 2: Does educational attainment impact employment status? Below is a table from the US Bureau of Labor Statistics' Current Population Survey Employment Status Men, 25+, Employed Men, 25+, Unemployed Less than a high school diploma 5,565 302 Educational attainment as of 2022 Some college or associate degree 17,722 556 16,801 564 2,934 188 High school graduates, no college (¹) 20,655 808 Bachelor's degree and higher Women, 25+, Employed 13,842 Women, 25+, Unemployed 614 (1) Includes persons with a high school diploma or equivalent. (2) Includes persons with bachelor's, master's, professional, and doctoral degrees. All numbers are in thousands - Source: https://www.bls.gov/cps/cpsaat07.htm 30,434 609 2. What is the test statistic? What is the p-value? 30,960 641 You will need to conduct a hypothesis test to determine if educational attainment and employment status are independent. 1. Write out the null and alternative hypothesis. Use correct notation. Clearly label the claim. 3. Write…arrow_forwardIf you are interested in how well students perform on a standardized math-achievement test after they have completed a six-week math unit in either a computer-assisted class, a videotaped course, or a regular classroom, what kind of design do you have?arrow_forward
- An insurance company offers four different deductible levels—none, low, medium, and high—for its homeowner's policyholders and three different levels—low, medium, and high—for its automobile policyholders. The accompanying table gives proportions for the various categories of policyholders who have both types of insurance. For example, the proportion of individuals with both low homeowner's deductible and low auto deductible is 0.07 (7% of all such individuals). Homeowner's Auto N L M H L 0.04 0.07 0.05 0.01 M 0.07 0.11 0.20 0.10 H 0.02 0.03 0.15 0.15 Suppose an individual having both types of policies is randomly selected. (a) What is the probability that the individual has a medium auto deductible and a high homeowner's deductible?(b) What is the probability that the individual has a low auto deductible? A low homeowner's deductible? auto deductible homeowner's deductible (c) What is the probability that the individual is in the same…arrow_forwardAn insurance company offers four different deductible levels—none, low, medium, and high—for its homeowner's policyholders and three different levels—low, medium, and high—for its automobile policyholders. The accompanying table gives proportions for the various categories of policyholders who have both types of insurance. For example, the proportion of individuals with both low homeowner's deductible and low auto deductible is 0.07 (7% of all such individuals). Homeowner's Auto N L M H L 0.04 0.07 0.05 0.04 M 0.07 0.09 0.20 0.09 H 0.02 0.03 0.15 0.15 Suppose an individual having both types of policies is randomly selected. (a) What is the probability that the individual has a medium auto deductible and a high homeowner's deductible?(b) What is the probability that the individual has a low auto deductible? A low homeowner's deductible? auto deductible homeowner's deductible (c) What is the probability that the individual is in the same…arrow_forwardAn insurance company offers four different deductible levels—none, low, medium, and high—for its homeowner's policyholders and three different levels—low, medium, and high—for its automobile policyholders. The accompanying table gives proportions for the various categories of policyholders who have both types of insurance. For example, the proportion of individuals with both low homeowner's deductible and low auto deductible is 0.07 (7% of all such individuals). Homeowner's Auto N L M H L 0.04 0.07 0.05 0.01 M 0.07 0.08 0.20 0.13 H 0.02 0.03 0.15 0.15 Suppose an individual having both types of policies is randomly selected. (d) Based on your answer in part (c), what is the probability that the two categories are different?(e) What is the probability that the individual has at least one low deductible level?(f) Using the answer in part (e), what is the probability that neither deductible level is low?arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL