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.

*H*_{0}: *μ*_{1} =
*μ*_{2} = *μ*_{3} =
*μ*_{4}

*H*_{a}: *μ*_{1} ≠
*μ*_{2} ≠ *μ*_{3} ≠
*μ*_{4}

*H*_{0}: *μ*_{1} =
*μ*_{2} = *μ*_{3} =
*μ*_{4}

*H*_{a}: Not all the population means are
equal.

*H*_{0}: *μ*_{1} ≠
*μ*_{2} ≠ *μ*_{3} ≠
*μ*_{4}

*H*_{a}: *μ*_{1} =
*μ*_{2} = *μ*_{3} =
*μ*_{4}

*H*_{0}: At least two of the population means are
equal.

*H*_{a}: At least two of the population means are
different.

*H*_{0}: Not all the population means are
equal.

*H*_{a}: *μ*_{1} =
*μ*_{2} = *μ*_{3} =
*μ*_{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?

Do not reject *H*_{0}. There is sufficient
evidence to conclude that the mean drying times for the four robots
are not all equal.

Reject *H*_{0}. There is not sufficient evidence
to conclude that the mean drying times for the four robots are not
all equal.

Do not reject *H*_{0}. There is not sufficient
evidence to conclude that the mean drying times for the four robots
are not all equal.

Reject *H*_{0}. 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 :

H_{0}: μ_{1} = μ_{2} = μ_{3} =
μ_{4}

H_{a}: Not all the population means are
equal.

Test statistics = 2.19

P-value = 0.1292

Do not reject *H*_{0}. There is not sufficient
evidence to conclude that the mean drying times for the four robots
are not all equal.

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