Sampling Distributions and the Central Limit Theorem:
The National Survey of Student Engagement asks college studentsquestions about the quality of their education. In 2018, NSSEreported the following result about college freshman:
During the current school year, about how often have you usednumerical information to examine a real-world problem or issue(unemployment, climate change, public health, etc.)?
Mean: 2.29 SD: .92
These results were based on a survey of over 500,000 studentsfrom 725 institutions. Suppose we want to see how Coker Collegestudents compare to the national results by taking independent,random samples of 35 students each. Find the mean μ_x ̅ andstandard deviation σ_x ̅ of this sampling distribution. (Hint: Usethe Central Limit Theorem)
Find the probability that the sample mean of a random sample of35 Coker College students for number of times using numericalinformation to examine real world issues is more than 3.
In this class, we've used numerical data to examine crime,genetic traits of fungus, political polling, and many otherreal-world topics. Would it be appropriate to say our statisticsclass sample of 19 students is unusual compared to the nationalaverage? Why or why not?
