Question

Mr. Tucker is reviewing data from an end of the year survey given to his school. The mean score for satisfaction at his school was
84
%
. He plans to randomly choose
5
sets of
10
surveys randomly from the school to calculate the mean score for each sample.



Which statement BEST describes the results Mr. Tucker should expect after calculating the mean scores for each sample?



A.
The sample means will differ slightly, but most will be close to
84
, the population mean.

B.
The sample means represent different groups, so the data will be different from the population mean.

C.
The sample means will always be lower than
84
because the sample sizes are smaller than the population.

D.
The sample means will be equal to the population mean because all students are part of the school population.

Answer 1

A.

Random samples will vary because of sampling variability, but the expected value of the sample mean equals the population mean (84%), so most of the sample means should be close to 84.