2. Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.15 to $3.45. Use the fact that the confidence interval for the mean has the form x – E to x + E to compute the sample mean and the maximal margin of error E.
4. Any state Auto Insurance Company took a random sample of 370 insurance claims paid out during a 1-year period. The average claim paid was $1570. Assume ó = $250. Find 0.90 and 0.99 confidence intervals for the mean claim payment.
5. Three experiments investigating the relationship between need for cognitive closure and persuasion were reported in “Motivated Resistance and Openness to Persuasion in the Presence or Absence of Prior Information” by A.W. Kruglanski (Journal of Personality and Social Psychology, Vol. 65, No. 5 pp. 861-874). Part of the study involved administering a “need for closure scale” to a group of students enrolled in an introductory psychology course. The “need for closure scale” has scores ranging from 101 to 201. For the 73 students in the highest quartile of the distribution, the mean score was x =178.70. Assume a population standard deviation of ó = 7.81. These students were all classified as high on their need for closure. Find a 95% confidence interval for the population mean score µ on the “need for closure scale” for all students with a high need for closure.
6. How large a sample is needed in Problem 5 if we wish to be 99% confident that the sample mean score is within 2 points of the population mean score for students who are high on the need for closure?
7. The Wind Mountain archaeological site is located in southwestern New Mexico. Wind Mountain was home to a culture of prehistoric Native Americans called Anasazi. A random sample of excavations at Wind Mountain gave the following depths (in centimeters) from present-day surface grade to the location of significant archaeological artifacts (Source: Mimbres Mogollon Archaeology, by A. Woosley and A. McIntyre, University of New Mexico Press):
85 45 120 80 75 55 65 60
65 95 90 70 75 65 68
a) Use a calculator with mean and sample standard deviation keys to verify thatx≈74.2 cm and s ≈18.3 cm.
b) Compute a 95% confidence interval for the mean depth µ at which archaeological artifacts from the Wind Mountain excavation site can be found.
8. Shards of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels found at the Wind Mountain archaeological site (see source in Problem 7). A random sample of ceramic vessels gave the following rim diameters (in centimeters):
15.9 13.4 22.1 12.7 13.1 19.6 11.7 13.5 17.7 18.1
a) Use a calculator with mean and sample standard deviation keys to verify that x ≈ 15.8 cm and s ≈ 3.5 cm.
b) Compute an 80% confidence interval for the population mean µ of rim diameters for such ceramic vessels found at the Wind Mountain archaeological site.