Question

The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time.com). The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.

Private Colleges

51.8	44.2	45.0	34.3	45.0
31.6	46.8	36.8	49.5	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

(a)

Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.)

sample mean $_____ thousand

sample standard deviation $____ thousand

Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.)

sample mean $______ thousand

sample standard deviation $_______ thousand

(b)

What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private − Public.)

$ ______ thousand

Interpret this value in terms of the annual cost (in dollars) of attending private and public colleges.

We estimate that the mean annual cost to attend private colleges is $_______ more than the mean annual cost to attend public college

(c)

Develop a 95% confidence interval (in thousand dollars) of the difference between the mean annual cost of attending private and public colleges. (Use Private − Public. Round your answers to one decimal place.)

$_______ thousand to $______ thousand

Answer 1

a)for private colleges

sample mean $42.70 thousand

sample standard deviation =$ 6.56 thousand

for public college

sample mean $22.30 thousand

sample standard deviation =$ 4.53 thousand

b)

point estimate=42.70-22.30 =20.40

We estimate that the mean annual cost to attend private colleges is 20.40 more than the mean annual cost to attend public college

c)

Point estimate of differnce =x1-x2=			20.400
for 95 % CI & 15 df value of t=			2.131
margin of error E=t*std error   =			5.2298
lower bound=mean difference-E=			15.1702
Upper bound=mean differnce +E=			25.6298
from above 95% confidence interval for population mean =(15.17,25.63)

95% confidence interval is 15.17  thousand to 25.63