Answered: Every 2 years, the National Assessment…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

In the previous question about the 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?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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