(1 point) The National Assessment of Educational Progress (NAEP) gave a test of

Question

(1 point) 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 u in the population of all young men. Consider the NAEP sample as an SRS from a Normal population with standard deviation ?-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 u 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 unknown mean . What is the missing number? (c) What is the 68% confidence interval for the population mean score ? based on this one sample? Note: Use the 68-95-99.7 rule to find the interval. on either side of the (a) 2.0702 to

Explanation / Answer

Solution:

We are given

Sample size = n = 840

Xbar = 272

Population standard deviation = ? = 60

Part a

Standard deviation of sampling distribution = ?/sqrt(n)

Standard deviation of sampling distribution = 60/sqrt(840)

Standard deviation of sampling distribution = 2.070196678

Answer: 2.0702

Part b

We know, according to the 68 part of the 68-95-99.7 rule, 68% of all values of xbar fall within one standard deviation from mean on either side of the unknown mean µ.

Here, 1*SD = 1*60 = 60

Answer: 60

Part c

68% confidence interval for population mean is given as below:

Confidence interval = Xbar ± 1*SD

Confidence interval = 272 ± 1*60

Confidence interval = 272 ± 60

Lower limit = 272 – 60 = 212

Upper limit = 272 + 60 = 332

Confidence interval = (212, 332)

Answer: 212 to 332

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