Question

**Wait-Times:** **USE SOFTWARE** There
are three registers at the local grocery store. I suspect the mean
wait-times for the registers are different. The sample data is
depicted below. The second table displays results from an ANOVA
test on this data with software.

Wait-Times in Minutes

x |
|||||||||

Register 1 | 2.0 | 2.0 | 1.1 | 2.0 | 1.0 | 2.0 | 1.0 | 1.3 | 1.55 |

Register 2 | 1.8 | 2.0 | 2.2 | 1.9 | 1.8 | 2.1 | 2.2 | 1.7 | 1.96 |

Register 3 | 2.1 | 2.1 | 1.8 | 1.5 | 1.4 | 1.4 | 2.0 | 1.7 | 1.75 |

ANOVA Results

F |
-valueP |

2.794 | 0.0840 |

**The Test:** Complete the steps in testing the
claim that there is a difference in mean wait-times between the
registers.

(a) What is the null hypothesis for this test?

*H*_{0}: *μ*_{1} ≠
*μ*_{2} ≠ *μ*_{3}.

*H*_{0}: *μ*_{2} >
*μ*_{3} >
*μ*_{1}.

*H*_{0}: At least one of the population means is
different from the others.

*H*_{0}: *μ*_{1} =
*μ*_{2} = *μ*_{3}.

(b) What is the alternate hypothesis for this test?

*H*_{1}: *μ*_{2} >
*μ*_{3} > *μ*_{1}.

*H*_{1}: *μ*_{1} ≠
*μ*_{2} ≠
*μ*_{3}.

*H*_{1}: At least one of the population means is
different from the others.

*H*_{1}: *μ*_{1} =
*μ*_{2} = *μ*_{3}.

(c) What is the conclusion regarding the null hypothesis at the
0.05 significance level?

reject *H*_{0}

fail to reject
*H*_{0}

(d) Choose the appropriate concluding statement.

We have proven that all of the mean wait-times are the same.

There is sufficient evidence to conclude that the mean wait-times are different.

There is not enough evidence to conclude that the mean wait-times are different.

(e) Does your conclusion change at the 0.10 significance level?

Yes

No

Answer #1

a) H0: μ1 = μ2 = μ3.

b) H1: At least one of the population means is different from the others

c) fail to reject H0

d) There is not enough evidence to conclude that the mean wait-times are different.

e) YES

since p value is smaller at 0.1 level of significance.

Wait-Times: There are three registers at the
local grocery store. I suspect the mean wait-times for the
registers are different. The sample data is depicted below. The
second table displays results from an ANOVA test on this data with
software.
Wait-Times in Minutes
x
Register 1
2.0
2.0
1.1
2.0
1.0
2.0
1.0
1.3
1.55
Register 2
1.8
2.0
2.2
1.9
1.8
2.1
2.2
1.7
1.96
Register 3
2.1
2.1
1.8
1.5
1.4
1.4
2.0
1.7
1.75
ANOVA Results...

Wait-Times (Raw Data, USE SOFTWARE):
There are three registers at the local grocery store. I suspect the
mean wait-times for the registers are different. The sample data is
depicted below. It gives the wait-times in minutes.
Register 1
Register 2
Register 3
2.0
1.8
2.1
2.0
2.0
2.1
1.1
2.2
1.8
2.0
1.9
1.5
1.0
1.8
1.4
2.0
2.1
1.4
1.0
2.2
2.0
1.5
2.1
2.2
The Test: Complete the steps in testing the
claim that there is a difference...

Wait-Times (Raw Data, Software Required):
There are three registers at the local grocery store. I suspect the
mean wait-times for the registers are different. The sample data is
depicted below. It gives the wait-times in minutes.
Register 1
Register 2
Register 3
2.0
1.8
2.1
2.0
2.0
2.1
1.1
2.2
1.8
2.0
1.9
1.5
1.0
1.8
1.4
2.0
2.1
1.4
1.0
2.2
2.0
1.3
2.0
1.7
The Test: Complete the steps in testing the
claim that there is a difference...

Wait-Times (Raw Data, Software Required):
There are three registers at the local grocery store. I suspect the
mean wait-times for the registers are different. The sample data is
depicted below. It gives the wait-times in minutes.
Register 1
Register 2
Register 3
2.0
1.8
2.1
2.0
2.0
2.1
1.1
2.2
1.8
2.0
2.6
1.5
1.0
1.8
1.4
2.0
2.1
1.4
1.0
2.2
2.0
1.4
1.9
1.8
The Test: Complete the steps in testing the
claim that there is a difference...

Wait-Times (Raw Data, Software Required):
There are three registers at the local grocery store. I suspect the
mean wait-times for the registers are different. The sample data is
depicted below. It gives the wait-times in minutes.
Register 1
Register 2
Register 3
2.0
1.8
2.1
2.0
2.0
2.1
1.1
2.2
1.8
2.0
2.6
1.5
1.0
1.8
1.4
2.0
2.1
1.4
1.0
2.2
2.0
1.8
2.1
2.0
The Test: Complete the steps in testing the
claim that there is a difference...

Travel-Times: There are three different ways I
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difference in mean travel-times between the three different ways.
The sample data is depicted below. The second table displays
results from an ANOVA test on this data with software. I claim
there is a difference in mean travel-times between the three
different routes.
Travel Times in Minutes
x
Interstate
23
24
22
22
21
20
22.0
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Tomato weights and Fertilizer (Raw Data, Software
Required):
Carl the farmer has three fields of tomatoes, on one he used no
fertilizer, in another he used organic fertilizer, and the third he
used a chemical fertilizer. He wants to see if there is a
difference in the mean weights of tomatoes from the different
fields. The sample data for tomato-weights in grams is given below.
Carl claims there is a difference in the mean weight for all
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Tomato weights and Fertilizer (Raw Data, Software
Required):
Carl the farmer has three fields of tomatoes, on one he used no
fertilizer, in another he used organic fertilizer, and the third he
used a chemical fertilizer. He wants to see if there is a
difference in the mean weights of tomatoes from the different
fields. The sample data for tomato-weights in grams is given below.
Carl claims there is a difference in the mean weight for all
tomatoes between the...

The following data summarize the results from an independent
measures study comparing three treatment conditions.
I
II
III
n = 6
n = 6
n =
6
M = 4
M = 5
M = 6
N = 18
T = 24
T = 30
T = 36
G = 90
SS = 30
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Use an ANOVA with α = .05 to determine whether there are
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You may need to use the appropriate technology to answer this
question.
Three different methods for assembling a product were proposed
by an industrial engineer. To investigate the number of units
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