##### Question

In: Statistics and Probability

# The average annual cost (including tuition, room, board, books, and fees) to attend a public college...

The average annual cost (including tuition, room, board, books, and fees) to attend a public college takes nearly a third of the annual income of a typical family with college age children. At private colleges, the average annual cost is equal to about to about 60% of the typical family’s income. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars. Private Colleges 52.8 43.2 45.0 33.3 44.0 30.6 45.8 37.8 50.5 42.0 Public Colleges 20.3 22.0 28.2 15.6 24.1 28.5 22.8 25.8 18.5 25.6 14.4 21.8 Using manual calculation to answer the following questions:

a. Compute the sample mean and the sample standard deviation for private and public collages

b. What is the point estimate of the difference between the population mean?

c. Interpret this value in terms of the annual cost of attending private and public colleges.

d. Develop a 95% confidence interval of the difference between the mean annual cost of attending private and public colleges.

## Solutions

##### Expert Solution

(a)

Private colleges: x-bar = 42.5, s = 6.9806

Public colleges: x-bar = 22.3, s = 4.5323

(b)

Point estimate = 42.5 - 22.3 = 20.2

(c)

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