Rapid drainage of floodwater is crucial to prevent damage during heavy rains. Several designs for a drainage canal were considered for a certain city. Each designs was tested five times, to determinehow longit took to drain the water in a reservoir. The following table pesents the drainage times, in minutes.Channel Type                      Drainage Time1                                       41.4  43.4  50.5  41.22                                       38.7   48.3  51.1  38.33                                       32.6   33.7  34.8   22.54                                       26.3    30.9  33.3   23.85                                       44.9    47.2   48.5   37.1a. Construct an ANOVA table.b. Can you conclude that there is a difference in the mean drainage times for the different channel designs? use the a=0.01 level of significance.

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Asked Dec 2, 2019
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Rapid drainage of floodwater is crucial to prevent damage during heavy rains. Several designs for a drainage canal were considered for a certain city. Each designs was tested five times, to determinehow longit took to drain the water in a reservoir. The following table pesents the drainage times, in minutes.

Channel Type                      Drainage Time

1                                       41.4  43.4  50.5  41.2

2                                       38.7   48.3  51.1  38.3

3                                       32.6   33.7  34.8   22.5

4                                       26.3    30.9  33.3   23.8

5                                       44.9    47.2   48.5   37.1

a. Construct an ANOVA table.

b. Can you conclude that there is a difference in the mean drainage times for the different channel designs? use the a=0.01 level of significance.

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Expert Answer

Step 1

(A)

According to the provided information, drainage time for the different channel design are given. Each drainage tested for 5 times.

There is only one factor which is drainage time. So, clearly it is a one way ANOVA.

Excel software is used to construct the ANOVA Table.

Software Procedure

Step by step procedure to calculate ANOVA using Excel.

  • Inter the data into worksheet
  • Go to DATA > Data Analysis
  • Anova : Single Factor
  • Select the data into Input Range
  • Select Grouped By: Row
  • Select Alpha 0.01
  • Click OK in each dialogue box.

The output of the ANOVA is shown below.

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Anova: Single Factor SUMMARY Sum Average Variance Groups Count Row 1 44.125 19.04917 4 176.5 Row 2 4 176.4 44.1 43.14667 4 123.6 Row 3 30.9 32.16667 Row 4 4 114.3 28.575 18.56917 Row 5 4 177.7 44.425 26.0625 ANOVA F crit Source of Variation SS df MS P-value Between Groups 1017.375 4 254.3438 9.14944 0.000598 4.89321 Within Groups 416.9825 15 27.79883 Total 1434.3575 19

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Step 2

B)   In order to conclude whether there is difference in the mean drainage t...

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$1t= *r1 = °ri = 3ri = 'rf :°H The Null hypothesis state that the mean drainage times for the different channel designs are same H At least one mean drainage times for the different channel designs is different

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