Answered: How long it takes paint to dry can have…

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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How long it takes paint to dry can have an impact on the production capacity of a business. An auto body & paint business invested in a paint-drying robot to speed up its process. An interesting question is, "Do all paint-drying robots have the same drying time?" To test this, suppose we sample five drying times for each of different brands of paint-drying robots. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. Suppose the following data were obtained.

Robot 1	Robot 2	Robot 3	Robot 4
128	143	134	150
138	134	143	143
134	143	138	134
124	147	137	139
141	128	128	154

At the ? = 0.05 level of significance, test to see whether the mean drying time is the same for each type of robot.

State the null and alternative hypotheses.

H₀: At least two of the population means are equal.
H_a: At least two of the population means are different.

H₀: ?₁ ≠ ?₂ ≠ ?₃ ≠ ?₄
H_a: ?₁ = ?₂ = ?₃ = ?₄

H₀: ?₁ = ?₂ = ?₃ = ?₄
H_a: Not all the population means are equal.

H₀: ?₁ = ?₂ = ?₃ = ?₄
H_a: ?₁ ≠ ?₂ ≠ ?₃ ≠ ?₄

H₀: Not all the population means are equal.
H_a: ?₁ = ?₂ = ?₃ = ?₄

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. There is not sufficient evidence to conclude that the mean drying times for the four robots are not all equal.

Reject H₀. There is sufficient evidence to conclude that the mean drying times for the four robots are not all equal.

Do not reject H₀. There is not sufficient evidence to conclude that the mean drying times for the four robots are not all equal.

Do not reject H₀. There is sufficient evidence to conclude that the mean drying times for the four robots are not all equal.

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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