The average annual cost (including tuition, room, board, books and fees) to atte

Question

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 (Money, April 2012). At private colleges, the average annua

a. Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places.

S1 =

S2 =

b. What is the point estimate of the difference between the two population means? Round your answer to one decimal place.

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

c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.

95% confidence interval, private colleges have a population mean annual cost $ to $ more expensive than public colleges.

I have the answers to (a) and (b) but I cannot figure out (c). Thanks!

Private Colleges 43.2 52.8 30.6 45.8 Public Colleges 22.0 20.3 25.8 45.0 37.8 28.2 18.5 33.3 50.5 15.6 25.6 44.0 42.0 24.1 14.4 28.5 21.8

Explanation / Answer

from the given data

from above

a)hence S1 =6.981 and S2 =4.532

b) point estimate =X1-X2 =20.200

C)as population std deviation not given; we will use t distribution

std error =(S12/n1+S22/n2)1/2 =2.566

here degree of freedom df =((S12/n1+S22/n2)2/((s12/n1)/(n1-1) +s22/n2)/(n2-1) ) =14.92 or 14

for 14 degree of freedom and 95% CI ; t =2.1448

hence confidence interval =estimated mean difference +/- t*std error =14.696 ; 25.704

95% confidence interval, private colleges have a population mean annual cost $14.696 to $25.704 more expensive than public colleges

S. no private public 1 52.8 20.3 2 43.2 22 3 45 28.2 4 33.3 15.6 5 44 24.1 6 30.6 28.5 7 45.8 22.8 8 37.8 25.8 9 50.5 18.5 10 42 25.6 11 14.4 12 21.8 total 425.000 267.600 mean 42.500 22.300 std deviation(S) 6.981 4.532

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