Answered: If we take many samples, the sample…

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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Question

The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test range from 00 to 500. Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem‑and‑leaf plot.

In 2019, 147,400 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was ?⎯⎯⎯=282.�¯=282. We want to estimate the mean score ?� in the population of all eighth‑graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation ?=40.

If we take many samples, the sample mean ?⎯⎯⎯�¯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score ?� in the population. What is the standard deviation of this sampling distribution?

Give your answer to four decimal places.

What is the standard deviation ?

According to the 95 part of the 68-95-99.7 rule, 95%of all values of ?⎯⎯⎯�¯ fall within how many points on either side of the unknown mean ??�? Give your answer to four decimal places.

What are the points?

Use the 95 part of the 68-95-99 rule to determine a 95% confidence interval for the population mean score ?� based on this one sample. Give your answers to at least two decimal places.

What is the lower bound ?

What is the upper bound ?

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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