Question

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
127	144	133	151
138	133	142	141
136	142	137	135
124	145	135	141
145	136	128	147

At the α = 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: μ₁ = μ₂ = μ₃ = μ₄
H_a: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄

H₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: Not all the population means are equal.  

H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄
H_a: μ₁ = μ₂ = μ₃ = μ₄

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

H₀: Not all the population means are equal.
H_a: μ₁ = μ₂ = μ₃ = μ₄

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?

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

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 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.

Answer 1

The statistical software output for this problem is :

H₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: Not all the population means are equal.  

Test statistics = 2.19

P-value = 0.1292

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