The National Assessment of Educational Progress (NAEP) gave atest of basic arithmetic and the ability to apply it in everydaylife to a sample of 840 men 21 to 25 years of age. Scores rangefrom 0 to 500; for example, someone with a score of 325 candetermine the price of a meal from a menu. The mean score for these840 young men was x???x¯ = 272. We want to estimate the mean score?? in the population of all young men. Consider the NAEP sample asan SRS from a Normal population with standard deviation ?? =60.
(a) If we take many samples, the sample mean x???x¯ varies fromsample to sample according to a Normal distribution with mean equalto the unknown mean score ?? in the population. What is thestandard deviation of this sampling distribution?
(b) According to the 99.7 part of the 68-95-99.7 rule, 99.7% of allvalues of x???x¯ fall within _______ on either side of the unknownmean ??. What is the missing number?
(c) What is the 99.7% confidence interval for the population meanscore ?? based on this one sample? Note: Use the 68-95-99.7 rule tofind the interval.
