According to U.S. News & World Report data, in 1995 tuition costs at Indiana University, a public university, were $2,984 per year, while the tuition costs at the University of Evansville, a private university in Indiana, were $11,800 per year. In that same year the average cost of tuition at all public U.S. colleges was $2,208, with a standard deviation of $1,041, and the average cost of tuition at all private U.S. colleges was $10,979.68, with a standard deviation of $4,057.

Question

According to U.S. News & World Report data, in 1995 tuition costs at Indiana University, a public university, were $2,984 per year, while the tuition costs at the University of Evansville, a private university in Indiana, were $11,800 per year. In that same year the average cost of tuition at all public U.S. colleges was $2,208, with a standard deviation of $1,041, and the average cost of tuition at all private U.S. colleges was $10,979.68, with a standard deviation of $4,057.

a. What is the z score for Indiana University?

b. What is the z score for the University of Evansville?

c. Which school was more expensive to attend in 1995, relative to the cost of education in its own category?

I am not sure how to work these.

Answer 1

Z = (score-mean)/SD

Which one has the highest Z score?

Answer 2

To find the z scores for Indiana University and the University of Evansville, we need to use the formula for calculating z scores:

z = (x - μ) / σ

where:
- z is the z score
- x is the value we want to standardize
- μ is the mean of the distribution
- σ is the standard deviation of the distribution

a. To calculate the z score for Indiana University:

z(Indiana University) = (tuition cost at Indiana University - average tuition cost at all public U.S. colleges) / standard deviation for public U.S. colleges

z(Indiana University) = ($2,984 - $2,208) / $1,041

b. To calculate the z score for the University of Evansville:

z(University of Evansville) = (tuition cost at the University of Evansville - average tuition cost at all private U.S. colleges) / standard deviation for private U.S. colleges

z(University of Evansville) = ($11,800 - $10,979.68) / $4,057

c. To determine which school was more expensive relative to its own category, we compare the z scores. A higher z score indicates a higher tuition cost relative to the average in that category.

If the z score for Indiana University is higher than the z score for the University of Evansville, then Indiana University was relatively more expensive compared to other public colleges. Conversely, if the z score for the University of Evansville is higher, then it was relatively more expensive compared to other private colleges.