Chapter 8, Problem 9CR

For Problems 8-12, categorize each problem according to the parameter being estimated: proportion p or mean µ. Then solve the problem.

Psychology: Closure 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 $\bar{x}=178.70$. Assume a population standard deviation of $\sigma =7.81$. These students were all classified as high on their need for closure. Assume that the 73 students represent a random sample of all students who are 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.