6
QuizMultiple Choice
Sampling Distributions – Center and Variability
Question 6 of 10 • NC-Math 4
A farmer determines that, on average, his chickens lay a total of 16 eggs each day. A random sample of 10 days was taken, and the mean number of eggs was 15.1 eggs. Let μ = the true mean number of eggs the chickens lay each day. Under the assumption that the true mean number of eggs is 16, 100 simulated means for samples of size 10 are shown in the dotplot.Using the dotplot, is there evidence that the chickens are laying fewer than 16 eggs?
Answer
A
Yes, since a sample mean number of eggs of 15.1 eggs or less only occurred twice in simulated values, there is evidence that the true mean number of eggs is less than 16.B
Yes, since a sample mean number of eggs of 15.1 is less than the mean number of eggs of 16, there is evidence to prove that the true mean number of eggs is less than 16.C
No, since a sample mean number of eggs of 15.1 is only 0.9 eggs less than a mean number of eggs of 16, there is insufficient evidence that the true mean number of eggs is less than 16.D
No, since a sample mean number of eggs of 15.1 never occurred in the dotplot, it is not possible that a random sample of 10 eggs will have a mean number of eggs of 15.1. Therefore, there is insufficient evidence that the true mean number of eggs is less than 16.