The National Assessment of Educational Progress (NAEP) gave a test of basic arit

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. According to the 95 part of the 68-95-99.7 rule, 95% of all values of ¯ x with a sample size of 840 fall within ____ on either side of the unknown mean . What is the missing number?

Explanation / Answer

here as std error =std deviation/(n)1/2 =60/(840)1/2 =2.07

as we know that 95% values fall with in 2 std deviation from mean

hence  95% of all values of ¯ x with a sample size of 840 fall within 2*2.07 =4.14 on either side of the unknown mean

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