Question

Every 2 years, the National Assessment of Educational Progress (NAEP) assesses nationally representative samples of students in public and private schools.  

The NAEP sample of 1077 students in grade 8 in public schools had a mean quantitative score = 275. Because the sample size is large, the sample s is close to the population standard deviation, σ, so take σ = 60.

Give a 95% confidence interval for the mean score μ in the population of all young adults.   Remember, we are now calculating a range of probable values around our estimate, with Confidence Interval = mean +/- z * (σ / sqrt(n) ), where  σ / sqrt(n) is the standard error of the sample mean.   

b. In the above NAEP survey, how does changing the sample size affect the margin of error of a confidence interval? For example, what are the margins of error for samples of size 250, or 4000, compared to 1077?

Answer 1

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