The National Assessment of Educational Progress (NAEP) gave a test of basic arit
ID: 3262683 • Letter: T
Question
The National Assessment of Educational Progress (NAEP) gave a test of basic arithmetic and the ability to apply it in everyday life to a sample of 840 men 21 to 25 years of age. Scores range from 0 to 500; for example, someone with a score of 325 can determine the price of a meal from a menu. The mean score for these 840 young men was x = 272. We want to estimate the mean score in the population of all young men. Consider the NAEP sample as an SRS from a Normal population with standard deviation = 60.
(b) According to the 99.7 part of the 68-95-99.7 rule, 99.7% of all values of x fall within _______ on either side of the unknown mean . What is the missing number?
(c) What is the 99.7% confidence interval for the population mean score based on this one sample? Note: Use the 68-95-99.7 rule to find the interval.
Explanation / Answer
n = 840, x-bar = 272, = 60
(b) The missing number is 3
(c)
n = 840
x-bar = 272
s = 60
% = 99.7
Standard Error, SE = /n = 60 /840 = 2.070196678
z- score = 2.967737925
Width of the confidence interval = z * SE = 2.96773792534179 * 2.07019667802706 = 6.143801194
Lower Limit of the confidence interval = x-bar - width = 272 - 6.1438011942975 = 265.8561988
Upper Limit of the confidence interval = x-bar + width = 272 + 6.1438011942975 = 278.1438012
The confidence interval is [265.86, 278.14]
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