Three experiements investigating the relation between need f

Three experiements investigating the relation between need for cognitive closure and persuation were performed. Part of the study involved administering a \"need for closure scale\" to a group of studnets enrolled ina n 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=176.50. Assume a population standard deviation of sigma= 7.87. These studnets were all classified as high on their need for closure. Assume that the 83 studnets represent a random sample of all studnets who are classified as high on their need for closure. How large a sampe is needed if we wish to be 99% confident that the sample mean score is within 2.0 oints of the population mean score for students whoar ehgih on the need for closure? (round youranswer up to the nearest whole number)
____ students

Solution

Given a=1-0.99 = 0.01, Z(0.005) = 2.58 (from standard normal table)

So n=(Z*s/E)^2

=(2.58*7.87/2)^2

=103.0692

Take n=104