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? Complete the table to show the statistical information the company has gathered. (2 points: 1 point for the company, 1 point for the information)

Company	CoSport Blockbuster
Sample size
Sample mean
Standard deviation of the distribution of sample means, \frac{\sigma }{{\sqrt n }}n.	0.4 (CoSport) 0.6 (Blockbuster)

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 identified in the answer to question 1 to complete the following table for the margins of error and confidence intervals at different confidence levels. Note: No further calculations are needed for the sample mean. (6 points: 2 points for each completed row)

Confidence level	Margin of error	Center of confidence interval (sample mean)	Lower boundary of confidence interval	Upper boundary of confidence interval
68%
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)