Question 16 - ANOVA 2To test whether the mean time to mix a batch of adhesive is the same for machines produced by four manufactures. Titebondmax obtained the attached data on the time (minutes) needed to mix the materials. Test whether the machines have equal mean mixing time at = 0.01. See attached data. **Data to Use**This table contains data collected from different manufacturers labeled A, B, C, and D. The figures represent certain values (possibly measurements, quantities, or performance metrics) associated with each manufacturer. | Manufacturer | A | B | C | D ||--------------|-----|-----|-----|-----|| | 25 | 23 | 25 | 27 || | 23 | 21 | 25 | 26 || | 21 | 23 | 25 | 27 || | 23 | 24 | 21 | 26 |**Explanation:**- Each row corresponds to a different entry from the data set.- Each column under a manufacturer lists several numbers, presumably indicating measurements or data points pertinent to that manufacturer. This format could be utilized for statistical analysis, comparison of performance metrics, or other educational purposes.

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Description: Question 16 - ANOVA 2To test whether the mean time to mix a batch of adhesive is the same for machines produced by four manufactures. Titebondmax obtained the attached data on the time (minutes) needed to mix the materials. Test whether the machine

ANOVA or Analysis of Variances is one of the most important fields in Statistic. The reason for this is that goes into the core of analyzing the variation exhibited samples, by breaking down the total variation into various different sources of variation. The most basic use of ANOVA is to test for the difference between the populations for several groups (2 or more). Let us recall that a t-test is used to compare the means of two groups, so then ANOVA is some sort extension that allows performing comparisons for two or more groups. As with any other hypothesis test, ANOVA uses a null and the alternative hypothesis. The null hypothesis is a statement that claims that all population means are equal, and the alternative hypothesis is the hypothesis that not all means are equal (observe that this does NOT imply that all means are unequal, it implies that al least one pair of means is unequal). The main assumptions required to perform a one-way ANOVA are: The dependent variable (DV) needs to be measured at least at the interval level The groups must come from normally distributed populations The groups must come from normal populations with equal population variances If the results of the ANOVA are significant, that is, the null hypothesis is rejected, we can perform a Post-Hoc test to assess exactly which pairs differ significantly. Examples of Post-Hoc tests are Fisher's LSD, Tukey's test, Bonferroni correction, etc. When some of the assumptions is not met (specifically the second are third), there are corrective options for some more robust statistics. When there are serious violations to the assumptions, it would be more appropriate to use a non-parametric alternative, like Kruskal-Wallis' Test. A one-way ANOVA compares two or more sample means, but if we want to compare two sample means, then it may be more efficient to use our t-test for two independent samples.

Answered: To test whether the mean time to mix a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Question 16 - ANOVA 2

To test whether the mean time to mix a batch of adhesive is the same for machines produced by four manufactures. Titebondmax obtained the attached data on the time (minutes) needed to mix the materials. Test whether the machines have equal mean mixing time at = 0.01. See attached data.

**Data to Use**

This table contains data collected from different manufacturers labeled A, B, C, and D. The figures represent certain values (possibly measurements, quantities, or performance metrics) associated with each manufacturer.

| Manufacturer | A | B | C | D |
|--------------|-----|-----|-----|-----|
| | 25 | 23 | 25 | 27 |
| | 23 | 21 | 25 | 26 |
| | 21 | 23 | 25 | 27 |
| | 23 | 24 | 21 | 26 |

**Explanation:**
- Each row corresponds to a different entry from the data set.
- Each column under a manufacturer lists several numbers, presumably indicating measurements or data points pertinent to that manufacturer.

This format could be utilized for statistical analysis, comparison of performance metrics, or other educational purposes.

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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