Answered: Dana is a math professor who usually…

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

Dana is a math professor who usually teaches in-person but has recently started teaching online. Suppose the average grade for the first exam for her in-person classes is 76.5 with a population standard deviation of 19.1. The first exam of her online class averaged just 68.4, based on 20 online exams. Dana wonders if her online students are worse than her in-person students or if the lower score is just random. Use a 95% confidence level to answer Dana’s question.

In answering this question, be sure to:

Show your work on the calculated score (you may copy/paste commands from Excel to do this);
Indicate what your calculated score is;
Indicate and justify what your critical score is; and
Determine if this sample average is statistically significant from the mean.

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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