Answered: Assume all the conditions of this test…

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 consumer group plans a comparative study of the mean life of four different brands of batteries. Ten batteries of each brand will be randomly selected and the time until the energy level falls below a pre-specified level is measured.

Transcribed Image Text:Assume all the conditions of this test have been met. Using the p-value from the output, what can we conclude at α = 0.01? **Analysis of Variance for Time:** | Source | df | SS | MS | F | P | |--------|----|--------|-------|-------|-----| | Brand | 3 | 365.28 | 121.76| 16.57 | 0.000 | | Error | 36 | 264.50 | 7.35 | | | | Total | 39 | 629.78 | | | | **Options for Conclusion:** 1. Fail to reject the null hypothesis and conclude that at least one mean differs from the other means. 2. Reject the null hypothesis and conclude that at least one mean differs from the other means. 3. Reject the null hypothesis and conclude that there is insufficient evidence to say that the means are not all equal. 4. Fail to reject the null hypothesis and conclude that there is insufficient evidence to say that the means are not all equal. **Explanation:** In this analysis of variance (ANOVA), we are given the following values: - **Degrees of freedom (df):** Represents the number of values that are free to vary. - **Sum of squares (SS):** Measures the total variability in the data. - **Mean square (MS):** An average of the squared deviations (SS divided by df). - **F-value:** A ratio of the variance explained by the model to the variance within the groups. - **P-value:** Indicates the probability of observing the F-value if the null hypothesis is true. Given the p-value of 0.000, which is less than α = 0.01, we can reject the null hypothesis and conclude that at least one brand mean differs from the others.

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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