Question

**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 in mean wait-times between the
registers.

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

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

*H*_{0}: *μ*_{2} >
*μ*_{3} >
*μ*_{1}.

*H*_{0}: *μ*_{1} =
*μ*_{2} = *μ*_{3}.

*H*_{0}: *μ*_{1} ≠
*μ*_{2} ≠ *μ*_{3}.

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

*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*_{2} >
*μ*_{3} > *μ*_{1}.

*H*_{1}: *μ*_{1} =
*μ*_{2} = *μ*_{3}.

(c) Use software to get the P-value of the test statistic (
*F* ). **Round to 4 decimal places unless your
software automatically rounds to 3 decimal places.**

P-value =

(d) What is the conclusion regarding the null hypothesis at the
0.01 significance level?

reject *H*_{0}

fail to reject
*H*_{0}

(e) 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.

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

Yes

No

Answer #1

EXCEL > DATA > DATA ANALYSIS > ANOVA: Single factor

a)

*H*0: *μ*1 = *μ*2 =
*μ*3.

b)

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

c)

P value = 0.0509

d)

P value > 0.01, Fail to reject H0

e)

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

f)

Yes, conclusion change at the 0.10 significance level

P value < 0.1, Reject H0

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

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...

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: 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
...

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...

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n = 6
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store is better when a manager is on-duty compared to when a
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Required):
Here we investigate whether the register balance at a local retail
store is better when a manager is on-duty compared to when a
manager is off-duty. Evidence like this might be used to determine
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