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Mathematics, 28.02.2020 05:21 nxusasmangaliso7596
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 μ in the population of all young men. Consider the NAEP sample as an SRS from a Normal population with standard deviation σ = 60. (a) If we take many samples, the sample mean x¯¯¯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population. What is the standard deviation of this sampling distribution? (b) According to the 68 part of the 68-95-99.7 rule, 68% of all values of x¯¯¯ fall within on either side of the unknown mean μ. What is the missing number? (c) What is the 68% confidence interval for the population mean score μ based on this one sample? Note: Use the 68-95-99.7 rule to find the interval.
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