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.
H
0: At least two of the population means are equal.
H
a: At least two of the population means are different.
H
0: ?1 ≠ ?2 ≠ ?3 ≠ ?4
H
a: ?1 = ?2 = ?3 = ?4
H
0: ?1 = ?2 = ?3 = ?4
H
a: Not all the population means are equal.
H
0: ?1 = ?2 = ?3 = ?4
H
a: ?1 ≠ ?2 ≠ ?3 ≠ ?4
H
0: 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 thep-value. (Round your answer to four decimal places.)
p-value =
What is your conclusion?
RejectH
0. There is not sufficient evidence to conclude that the mean drying times for the four robots are not all equal.
RejectH
0. There is sufficient evidence to conclude that the mean drying times for the four robots are not all equal.
Do not rejectH
0. There is not sufficient evidence to conclude that the mean drying times for the four robots are not all equal.
Do not rejectH
0. There is sufficient evidence to conclude that the mean drying times for the four robots are not all equal.