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Three experiments investigating the relation between need for cognitive closure and persuasion were performed.

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 83 students in the highest quartile of the distribution, the mean score was x = 176.70. Assume a population standard deviation of σ = 7.57. These students were all classified as high on their need for closure. Assume that the 83 students represent a random sample of all students who are classified as high on their need for closure. How large a sample is needed if we wish to be 99% confident that the sample mean score is within 1.5 points of the population mean score for students who are high on the need for closure? (Round your answer up to the nearest whole number.) PLEASE SHOW WORK

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