8. One year, there were about 4.600 higher education institutions in the U.S. As

Question

8. One year, there were about 4.600 higher education institutions in the U.S. As part ofa continuing study of higher education, the Carnegic ommission took a simple random sample of 400 of these institutions. The average enrollment in the 400 sample schools was 3.700. and the SD was 6.600 f i) (6 pls) Fill in lhe hlanks with numbers. An approvinate 68% confidence interval lor the average enle of all 4.600 instiuons runs from to ii) (3 pts) 50vey organizalions are sent oul to estiate the averae cnrllment of all 4.600 institutions. Each of them takes an SRS of 400 institutions and constructs a 68% confidence interval. I low many of these 50 con lidence inten als cover the populationverage? iii) ( 4 pis) True or fals. an I explain: .. I here is a 95% chance lhal lhe population average is 2SEs rom the av erage enrollment of the 400 sample schools. iv) (3 pts) True or lalse: "when normal curve is heing used on the probability histogram ftmple arage to igure conlidence levels.t doesn't atter whether the original data follow the normal curve."

Explanation / Answer

i)

68% of data lies within 1 standard deviation

hence

lower bound = 3700 - 6600 = 0

upper bound = 3700 + 6600 = 10300

ii)

68% of data is within one standard deviation

number of intervals cover population average

= 50 * 68%

= 34

iii)

true , 95% of data lies within 2 standard deviations

iv)

False

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