ONLY NEED THE LAST 2 QUESTIONS (POST HOC A AND B)PROBLEM 1 – TESTING PAINT BRAND CLAIMSSituation:Does a paint brand matter? Four different paint brands advertised for the same type of paint that they have the same drying time. To check the manufacturer’s claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded.Action:Use the following data and ANOVA to test whether there is a significant difference in mean drying time among the paint brands. Use significance level of 5%. Discuss the business implications of the findings.Paint Brand 1Paint Brand 2Paint Brand 3Paint Brand 4128144133150137133143142135142137135124146136140141130131153Ho (Null Hypothesis): There is no significant difference in drying time of paints. Ha (Alternate Hypothesis): There is a significant difference in drying time of paints.P-Value = 0.0928Since the P-Value is greater than the level of significance, Ho should not be rejected (fail to reject the null hypothesis).It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that there is a significant difference in mean drying time among the paint brands, at the α=0.05 significance level.If you obtain a significant F statistic, run a Post-Hoc Comparison's test on the four means to answer this question. You can select whichever Post-Hoc Comparison procedure you desire. If none exists on your software, do individual t-tests on all pairs of means. WHAT POST-HOC COMPARISON TEST USED? STATE THE CONCLUSION DRAWN BASED POST-HOC COMPARISON TEST COMPLETED

1. For the situation, Tukey's Post Hoc test is used for post-hoc comparisons. 2. Excel Procedure for ANOVA: Enter the data for Brand 1, Brand 2 and Brand 3, Brand 4 in Excel sheet. Go to Data Click on Data Analysis. Select ‘Anova:single factor’ and click on ‘OK’ Select P1:S6 under ‘input range’. Click on ‘OK’. Excel Output: From the Excel output, The mean for Brand 1 is 133 and the size is 5. The mean for Brand 2 is 139 and the group size is 5. The mean for Brand 3 is 136 and the group size is 5. The mean for Brand 4 is 144 and the group size is 5. The mean square within groups is 43.25Critical Value: From the given information, there are 4 groups and the total number of observations is 20. From Tukey’s table, the value QU corresponding with k=4, error degrees of freedom as 16 and 0.05 level of significance is 4.05. Rejection Rule: If the test statistic is greater than the critical value, then the pairs of means are significant. If the test statistic is less than or equal to the critical value, then the pairs of means are not significant. Pair Test statistic,HSD=Mi-MjMSwnh Critical value Decision Conclusion Brand 1 VS Brand 2 133-13943.255=2.04 4.05 Test statistic <critical value Not significant Brand 1 VS Brand 3 133-13643.255=1.02 4.05 Test statistic <critical value Not significant Brand 1 VS Brand 4 133-14443.255=3.74 4.05 Test statistic <critical value Not significant Brand 2 VS Brand 3 139-13643.255=1.02 4.05 Test statistic <critical value Not significant Brand 2 VS Brand 4 139-14443.255=1.70 4.05 Test statistic <critical value Not significant Brand 3 VS Brand 4 136-14443.255=2.72 4.05 Test statistic <critical value Not significant In the given situation, there are no significant pairs in the data.

Answered: ONLY NEED THE LAST 2 QUESTIONS (POST…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

ONLY NEED THE LAST 2 QUESTIONS (POST HOC A AND B)

PROBLEM 1 – TESTING PAINT BRAND CLAIMS

Situation:

Does a paint brand matter? Four different paint brands advertised for the same type of paint that they have the same drying time. To check the manufacturer’s claims, five samples were tested for each of the paints. The time in minutes until the paint was dry enough for a second coat to be applied was recorded.

Action:

Use the following data and ANOVA to test whether there is a significant difference in mean drying time among the paint brands. Use significance level of 5%. Discuss the business implications of the findings.

Paint Brand 1	Paint Brand 2	Paint Brand 3	Paint Brand 4
128	144	133	150
137	133	143	142
135	142	137	135
124	146	136	140
141	130	131	153

Ho (Null Hypothesis): There is no significant difference in drying time of paints. Ha (Alternate Hypothesis): There is a significant difference in drying time of paints.
P-Value = 0.0928
Since the P-Value is greater than the level of significance, Ho should not be rejected (fail to reject the null hypothesis).
It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that there is a significant difference in mean drying time among the paint brands, at the α=0.05 significance level.

If you obtain a significant F statistic, run a Post-Hoc Comparison's test on the four means to answer this question. You can select whichever Post-Hoc Comparison procedure you desire. If none exists on your software, do individual t-tests on all pairs of means.

WHAT POST-HOC COMPARISON TEST USED?
STATE THE CONCLUSION DRAWN BASED POST-HOC COMPARISON TEST COMPLETED

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 + ...

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Anova and Design of Experiments$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.