Question

2. Four chemical plants discharge effluents into streams in the vicinity of their locations. To determine if there is any difference in the extent of pollution created by the effluents, five samples of liquid waste were collected from each plant. The data collected is as follows: Plant Polluting Effluents (lb/gal of waste) A 1.65 1.72 1.50 1.37 1.60 B 1.70 1.85 1.46 2.05 1.80 C 1.40 1.75 1.38 1.65 2.00 D 2.10 1.95 1.65 1.88 2.00 (a) Use the Anova: Single Factor tool from the Analysis Toolpak in Microsoft Excel to perform a one-way ANOVA on the above data. (b) Do the data provide sufficient evidence to indicate a difference in the mean weight of effluents per gallon in the effluents discharged from the four plants? Test using α = 0.05.

Answer 1

Answer:-

Given That:-

2. Four chemical plants discharge effluents into streams in the vicinity of their locations. To determine if there is any difference in the extent of pollution created by the effluents, five samples of liquid waste were collected from each plant. The data collected is as follows: Plant Polluting Effluents (lb/gal of waste) A 1.65 1.72 1.50 1.37 1.60 B 1.70 1.85 1.46 2.05 1.80 C 1.40 1.75 1.38 1.65 2.00 D 2.10 1.95 1.65 1.88 2.00.

Given,

Here the null hypothesis to be tested is

i.e the means are same.

And the alternative hypothesis is

: At least one mean is different.

(a) Use the Anova: Single Factor tool from the Analysis Toolpak in Microsoft Excel to perform a one-way ANOVA on the above data.

To perform ANOVA in Excel

Step 1:

Enter the data

Step 2:

Data > Analyse > Data Analysis

click on ANOVA Single Factor > OK

Step 3:

Inout the range, grouped by Rows, and α = 0.05

Then we will get the following output

(b) Do the data provide sufficient evidence to indicate a difference in the mean weight of effluents per gallon in the effluents discharged from the four plants? Test using α = 0.05.

Here the p - value is 0.0639, which is greater than the significance level specified. So, The decision is failed to reject the null hypothesis.

i.e,

The data does not provide sufficient evidence to indicate a difference in the mean weight.

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