Question

Ms. Rivera is analyzing results from a district-wide reading assessment.The mean score for the entire district (the population mean) is 72 points.
She decides to randomly select 6 samples, each consisting of 15 students, and calculate the mean score for each sample. Which statement BEST describes the results Ms. Rivera should expect from her sample means?
A. The sample means will vary slightly, but most will be close to 72, the population mean.
B. The sample means will be very different from each other because each sample contains different students.
C. The sample means will always be higher than 72 because sample sizes are smaller than the population.
D. The sample means will be exactly 72, since all students come from the same district.

Answer 1

A. The sample means will vary slightly, but most will be close to 72, the population mean.

Reason: Sample means are unbiased estimates of the population mean, so their average equals 72. They will vary from sample to sample, but with sample size 15 the variation (standard error = σ/√15) is limited, so most sample means cluster around 72. Options B, C, and D are incorrect for the reasons above.