Question

College tuition: A simple random sample of 35 colleges and universities in the United States has...

College tuition: A simple random sample of 35 colleges and universities in the United States has a mean tuition of $17,800 with a standard deviation of $10,400. Construct a 98% confidence interval for the mean tuition for all colleges and universities in the United States.

A 98% confidence interval for the mean tuition for all colleges and universities is x<u<x

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

sample mean = = 17800

Population standard deviation =    = 10400

Sample size = n =35

At 98% confidence level the z is ,

Z/2 = Z0.01 = 2.326


Margin of error = E = Z/2 * ( /n)

= 2.326 * ( 10400 /   35)

= 4088.9
At 95% confidence interval mean
is,

- E < < + E

17800-1088.9 <   < 17800+4088.9

16711.1 <   < 21888.9

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