Assume I work in the testing department of my local universityand I am intereste

Question

Assume I work in the testing department of my local universityand I am interested in knowing something about the university'sstudents average I.Q. I have a limited budget so I take a randomsample of 50 from the population of students (N=2000). The averageI.Q. in this sample is 101.2 and the standard deviation of thesample is 9. Historical data tells me that the average I.Z. of myuniversity's students is 100. Can both the 100 and the 101.2 exist in the same population(this particular university)? Why or why not? Use the concepts (sample theory) to answer this. Assume I work in the testing department of my local universityand I am interested in knowing something about the university'sstudents average I.Q. I have a limited budget so I take a randomsample of 50 from the population of students (N=2000). The averageI.Q. in this sample is 101.2 and the standard deviation of thesample is 9. Historical data tells me that the average I.Z. of myuniversity's students is 100. Can both the 100 and the 101.2 exist in the same population(this particular university)? Why or why not? Use the concepts (sample theory) to answer this.

Explanation / Answer

The distribution of the sample mean is N(100,9/50) or approx N(100, 1.27) by the Central LimitTheorem. The sample average of 101.2 is not very unusual as it fallswithin one standard error of the mean. The value 100, is thevalue of the the population mean whereas the value 101.2 is thesample mean.They both can certainly exist in the same population.If we take more samples of size 50, they will tend to clusteraround 100. Some slightly more, some slightly less

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