The distribution of room and board expenses per year at a four-year college is normally distributed with a mean of $5850 and standard deviation of $1125. Random samples of size 20 are drawn from this population
And the mean of each sample is determined. Which of the following mean expenses would be considered
Unusual?
A)$5180
B)$6350
C)$6180
D)none of these

Question

Quizplus · Accepted Answer

To determine whether a mean is considered unusual, we need to calculate its z-score:

z = (sample mean - population mean) / (standard deviation/sqrt(sample size))

For choice A,

z = (5180 - 5850) / (1125/sqrt(20)) = -2.10

A z-score of -2.10 means that the sample mean is 2.10 standard deviations below the population mean. This falls in the range of about the bottom 2.5% of the distribution.

Using a standard significance level of 0.05 or 5%, we would consider sample means that fall outside of the range of +/- 1.96 standard deviations to be unusual, or about the bottom or top 2.5% of the distribution.

Therefore, choice A with a z-score of -2.10 would be considered unusual. Choices B and C both fall within the range of +/- 1.96 standard deviations, so they would not be considered unusual.

The Distribution of Room and Board Expenses Per Year at a Four-Year