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AssignmentMultiple Select

Sampling Distributions – Center and Variability

Question 1 • NC-Math 4

Which explanations are justified based on the evidence you obtained? Check all that apply.

Answer
A
It is possible that the population mean is 3.53, but the sample result is greater than that due to sampling variability.
B
It is possible that the school administrator made a mistake, and the population mean is greater than 3.53.
C
The fact that the sample mean is greater than the claimed population mean proves that the average GPA of the senior class is greater than 3.53
D
The sample mean of 3.70 cannot be correct because the claimed population mean is 3.53.
E
The population mean of 3.53 cannot be correct because the calculated sample mean is 3.70.

Explanation

A sample mean of 3.70 does not have to equal the population mean of 3.53; samples vary, so this difference could be due to sampling variability. It is also possible that the administrator’s claimed value is mistaken and the population mean is greater than 3.53. The sample mean alone does not prove the population mean is greater, nor does it show that either value is impossible.

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