The average cost of tuition, room and board at community colleges is reported to be $8,500 per year with a standard deviation of $1,200, but a financial administrator believes that the average cost is higher. A study conducted using 150 community colleges showed that the average cost per year is $9,000. Let $\alpha$ = 0.05. Given the z-statistic is 5.1, what is our decision about the average cost?
A) Equal to $8,500
B) Greater than $8,500
C) Less than $8,500
D) Not equal to $8,500

Question

Quizplus · Accepted Answer

The z-statistic of 5.1 is a measure of how many standard deviations the sample mean of $9,000 is from the population mean of $8,500. A large positive z-statistic like this indicates that the sample mean is significantly higher than the population mean. Since our null hypothesis is that the population mean is $8,500, and the alternative hypothesis is that it is greater than $8,500, we would reject the null hypothesis at a significance level of 0.05 and conclude that the average cost is greater than $8,500. Therefore, the best choice is B: Greater than $8,500.

The Average Cost of Tuition, Room and Board at Community α\alphaα

The Average Cost of Tuition, Room and Board at Community $\alpha$