Chapter 6: Q61E (page 338)
Short Answer
Answer
- 1.645
- 2.576
- 1.960
4 1.28
Chapter 6: Q61E (page 338)
Answer
4 1.28
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Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 5.44 (p. 320). The researchers obtained a random sample of 106 social robots through a Web search and determined that 63 were designed with legs, but no wheels.
a. Find a 99% confidence interval for the proportion of all social robots designed with legs but no wheels. Interpret the result.
b. In Exercise 5.42, you assumed that 40% of all social robots are designed with legs but no wheels. Comment on the validity of this assumption.
A random sample of 50 consumers taste-tested a new snack food. Their responses were coded (0: do not like; 1: like; 2: indifferent) and recorded as follows:

a. Use an 80% confidence interval to estimate the proportion of consumers who like the snack food.
b. Provide a statistical interpretation for the confidence interval you constructed in part a.
Facial structure of CEOs. In Psychological Science (Vol. 22, 2011), researchers reported that a chief executive officer’s facial structure can be used to predict a firm’s financial performance. The study involved measuring the facial width-to-height ratio (WHR) for each in a sample of 55 CEOs at publicly traded Fortune 500 firms. These WHR values (determined by a computer analyzing a photo of the CEO’s face) had a mean of and a standard deviation of .
a. Find and interpret a 95% confidence interval for , the mean facial WHR for all CEOs at publicly traded Fortune 500 firms.
b. The researchers found that CEOs with wider faces (relative to height) tended to be associated with firms that had greater financial performance. They based their inference on an equation that uses facial WHR to predict financial performance. Suppose an analyst wants to predict the financial performance of a Fortune 500 firm based on the value of the true mean facial WHR of CEOs. The analyst wants to use the value of . Do you recommend he use this value?
Monitoring phone calls to a toll-free number. A largefood-products company receives about 100,000 phone callsa year from consumers on its toll-free number. A computermonitors and records how many rings it takes for an operatorto answer, how much time each caller spends “on hold,” andother data. However, the reliability of the monitoring systemhas been called into question by the operators and their labour unions. As a check on the computer system, approximatelyhow many calls should be manually monitored during thenext year to estimate the true mean time that callers spend onhold to within 3 seconds with 95% confidence? Answer thisquestion for the following values of the standard deviation ofwaiting times (in seconds): 10, 20, and 30.
College dropout study. Refer to the American Economic Review (December 2008) study of college dropouts, Exercise 2.79 (p. 111). Recall that one factor thought to influence the college dropout decision was expected GPA for a student who studied 3 hours per day. In a representative sample of 307 college students who studied 3 hours per day, the mean GPA was and the standard deviation was . Of interest is, the true mean GPA of all college students who study 3 hours per day.
a. Give a point estimate for .
b. Give an interval estimate for . Use a confidence coefficient of .98.
c. Comment on the validity of the following statement: “98% of the time, the true mean GPA will fall in the interval computed in part b.”
d. It is unlikely that the GPA values for college students who study 3 hours per day are normally distributed. In fact, it is likely that the GPA distribution is highly skewed. If so, what impact, if any, does this have on the validity of inferences derived from the confidence interval?
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