The average annual cast (induding tuition, rnom, hoard, honks and fees) to attan

Question

The average annual cast (induding tuition, rnom, hoard, honks and fees) to attand a public college takes nearly a third af the annual incame of a typical family with college-aga children (Money, April 7012) At private colleges, the average annual cost is equal to about 6% tvpical family's income. The following random samples show the annual cust of attending private and public colleges. Data are in thousands of dollars. Clitk on the webfile logo to reference the data. WEB Private Colleges 52.8 30.6 43 2 45.8 45.0 37.8 33.3 50.5 44.0 42.0 Public Colleges 20.3 22.8 22.0 25.8 28.2 18.5 15.6 25.6 24.1 14.4 28.5 21.8 a. Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places 1-6.98 b. What is the paint estimate of the difference betweern the two population means? Round your answer to one decimal place. 0.3 Interpret this value in terms of tha annual cost of attending private and public colleges 20200 c. Develop 95% confidence interval of the difference between the annual cost uf attending private and pubic colleges. 95% confidence interval, private colleges have a populatin mean annual cost mure expenisive Lhan public colleges. Hide Feed back Partially Correct Faedhack Sec Inferences about the Difference between Two population Means: 1 and 2 unknown. Check My Exercise 10.13 Question Save Exit Submit Assignment for G

Explanation / Answer

Ans :   CI [18.538, 21.862]

Pooled Variance
s2p = (SS1 + SS2) / (df1 + df2) = 69.24 / 20 = 3.46

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2)) = ((3.46/10) + (3.46/12)) = 0.8

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2) = 20.2 ± (2.09 * 0.8) = 20.2 ± 1.662

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