Question

# How long it takes paint to dry can have an impact on the production capacity of...

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
Ha: μ1μ2μ3μ4

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

H0: μ1μ2μ3μ4
Ha: μ1 = μ2 = μ3 = μ4

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

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

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

p-value =

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.

The statistical software output for this problem is :

H0: μ1 = μ2 = μ3 = μ4
Ha: 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.