A test is given n = 4 times across different sections of a course. The scores on a test are normally distributed with an average (mean) of 72 and a standard deviation of 4 points. Construct a 90% and 95% confidence interval for the true mean test score. Interpret the confidence interval in your own words.Do you think this test is fair based on the confidence interval? Why or why not?

The following information has been provided: The sample size is n=4. The sample mean is x¯=72. The…

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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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A test is given n = 4 times across different sections of a course. The scores on a test are

normally distributed with an average (mean) of 72 and a standard deviation of 4 points.

Construct a 90% and 95% confidence interval for the true mean

test score.

Interpret the confidence interval in your own words.
Do you think this test is fair based on the confidence interval? Why or why not?

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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