Three experiments investigating the relation between need forcognitive closure and persuasion were performed. Part of the studyinvolved administering a \"need for closure scale\" to a group ofstudents enrolled in an introductory psychology course. The \"needfor closure scale\" has scores ranging from 101 to 201. For the 76students in the highest quartile of the distribution, the meanscore was x = 178.10. Assume a population standard deviation of σ =8.21. These students were all classified as high on their need forclosure. Assume that the 76 students represent a random sample ofall students who are classified as high on their need for closure.How large a sample is needed if we wish to be 99% confident thatthe sample mean score is within 2.1 points of the population meanscore for students who are high on the need for closure? (Roundyour answer up to the nearest whole number.)
