Statistical Truth of Fiction
The Marjin-O’Heara, a polling and research corporation, creates reports to help different companies design and market new products. The Marjin-O’Heara’s two most recents clients are oSport and Blockbuster Entertainment. CoSport is planning to introduce a new basketball jersey design. Blockbuster Entertainment is releasing a sequel to a popular movie. Choose one of the reports and use statistical analysis to evaluate Marjin-O’Heara’s conclusions. Choose your report!
[A basketball jersey is shown above the text “The Jersey.” Click.]
The Jersey Report
Marjin-O’Heara is investigating the color of the new jersey for a basketball team. The firm collected survey data from 400 fans after a game at the stadium and asked them to rate the color from 0 to 10 (where 0 is strongly dislike and 10 is strongly like). The data showed that the new color scored a sample average of 6.5. The sample standard deviation of the survey data was 0.4. Based upon the findings, Marjin-O’Heara recommended that CoSport put the new jerseys into production. In your assignment, you’ve been called in to analyze the data and evaluate the company’s finding.
[A picture of a frighten girl is shown above the text “The Sequel.” Click.]
The Sequel Study
Marjin-O’Heara is conducting an investigation to help its client decide whether to bring back a character in a sequel to a popular action film. The firm collected survey data from 900 fans who streamed the original film online, asking viewers to rate the character from 0 to 10 (where 0 is strongly dislike and 10 is strongly like). The character scored a sample average of 4.6 on the likability scale, with a sample standard deviation of 0.6. Based on the findings, Marjin-O’Heara recommended that Blockbuster Entertainment not include the character in the upcoming sequel. In your assignment, you’ve been called in to analyze the data and evaluate the company’s findings.
Statistical Truth or Fiction
Marjin-O’Heara, a polling and research company, has created a recommendation report for your company to help with the design and marketing of a new product. Your company is looking for a likability score in the general population of at least 5.2, with a confidence level of 95%. You’ve been called in to analyze the data and evaluate Marjin-O’Heara’s findings.
Your Report Data
1. What company are you working for? List the statistical information the company has gathered. (2 points: 1 point for the company, 1 point for the information)
Creating a Data Model
2.To help evaluate the original report, draw a normal curve for the data Marjin-O’Heara collected. Include the values of the mean and the first three standard deviations in your sketch. (4 points: 1 point for the curve, 3 points for correct critical values)
3. The client was hoping for a likability score of at least 5.2. Use your sample mean and standard deviation to complete the following table for the margins of error and confidence intervals at different confidence levels. (6 points: 2 points for each completed row)Confidence levelMargin of errorCenter of confidence interval (sample mean)Lower boundary of confidence intervalUpper boundary of confidence interval68% 95% 99.7%
4. Your company has stated that it prefers to base its decisions on information that has a 95% confidence level. From the values in your table, what is the margin of error for your sample mean at 95%? What is the confidence interval for your sample mean at 95%? Is the company’s likability goal within or below the appropriate confidence interval? (4 points: 3 points for margin of error and confidence interval, 1 point for goal on interval)
Evaluating Your Company’s Decisions
5. Part of your report involves evaluating the experimental design used by Marjin-O’Heara. Can you find any problems with the method of sampling that may have introduced some level of bias? (2 points: 2 points for the discussion of bias)
6. Based on your company’s criteria for decision making and your analysis of bias in the research report done by Marjin-O’Heara, do you think the company made the correct decision? Why or why not? (2 points: 1 point for the decision, 1 point for the explanation)