Homework 9a While writing an article on the high cost of college education, a re

Question

Homework 9a

While writing an article on the high cost of college education, a reporter took a random sample of the cost of new textbooks for a semester. The random variable x is the cost of one book. Her sample data can be summarized by the following. (Give your answers correct to two decimal places.)

n = 39, x = 3621.6, and (x - x)2 = 9685.4

(a) Find the sample mean, x.
$  

(b) Find the sample standard deviation, s.
$  

(c) Find the 98% confidence interval to estimate the true mean textbook cost for the semester based on this sample.

Explanation / Answer

Solution:

Given that

n = 27, x = 3621.6, and (x - x)^2 = 9685.4

a) Sample mean = 3621.6/27 = 134.13

b) SD = sqrt(9685.4/26) = 19.30

c) Confidence interval :

ME = 1.645(19.30)/sqrt(27) = 6.11

CI: 134.13 - 6.11 < < 134.13 + 6.11

128.02 < < 140.24

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