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⎯⎯⎯x¯ = 272. We want to estimate the mean score μμ in the population of all young men. Consider the NAEP sample as an SRS from a Normal population with standard deviation σσ = 60.

a If we take many samples, the sample mean x⎯⎯⎯x¯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μμ in the population. What is the standard deviation of this sampling distribution?

b According to the 99.7 part of the 68-95-99.7 rule, 99.7% of all values of x⎯⎯⎯x¯ fall within _______ on either side of the unknown mean μμ. What is the missing number?

c What is the 99.7% confidence interval for the population mean score μμ based on this one sample? Note: Use the 68-95-99.7 rule to find the interval.

Answer 1

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