Answered: A statistics professor gave an exam on…

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 statistics professor gave an exam on performing the T-Test with σ unknown. The exam had the bonus question "Guess the average score on this final exam. If a T-Test is performed and the mean guess for the class is not significantly different from the true average exam score, everyone in the class will then receive two bonus points." There were 10 students that took the final exam. The true average exam score was 89.3. The professor conducts a one-mean hypothesis at the 5% significance level, to test if the mean guess for the class is not significantly different from the true average exam score of 89.3. For this test: H0:μ=89.3; Ha:μ≠89.3, which is a two-tailed test. Student guesses are given below. Use a TI-83, TI-83 Plus, or TI-84 calculator to test whether the students should receive the two bonus points. Identify the test statistic, t, and p-value from the calculator output, rounding to two decimal places. 92 85 84 70 80 85 99 72 91 82

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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