A researcher records a sample of 30 exam scores and finds that the population mean for these data is larger than the sample variance.Is this possible?
A)yes,the population variance is usually larger than the sample variance
B)no,the population variance will only be larger when at least 50 scores are recorded
C)no,the sample variance will be larger because SS is divided by degrees of freedom in the denominator of the variance formula
D)not possible to know because the scores are not given

Question

Quizplus · Accepted Answer

The sample variance formula divides the sum of squares by the degrees of freedom, which is always n-1 for a sample of size n. This means that the sample variance will always be larger than the population variance, which is calculated by dividing the sum of squares by the population size. Therefore, it is not possible for the population mean to be larger than the sample variance.

A Researcher Records a Sample of 30 Exam Scores and Finds