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

52.8	44.2	45.0	34.3	45.0
29.6	46.8	38.8	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)

sample mean for private colleges =42.80

sample standard deviation =6.96

sample mean for public colleges =22.30

sample standard deviation =4.53

b)

Point estimate =x1-x2=

20.500 thousand

We estimate that the mean annual cost to attend private colleges is 20500 more than the mean annual cost to attend public college

c)

standard error se=√(S21/n1+S22/n2)=

2.5598

Point estimate of differnce =x1-x2=			20.500
for 95 % CI & 14 df value of t=			2.145
margin of error E=t*std error   =			5.4902
lower bound=mean difference-E=			15.0098
Upper bound=mean differnce +E=			25.9902
from above 95% confidence interval for population mean =15.01 thousand to 25.99 thousand