Question

2. A food processing plant typically contain fungus spores. If the ventilation system is not adequate, this can have a serious effect of the health of employees. To determine the amount of spores present, random air samples are pumped to a certain plate, and the number of "colony-forming units (CFUs)" are determined after time allowed for incubation. The data from the room of a plant that slaughters 35,000 turkeys per day, which are obtained during the four seasons of the year, is given below. The units are in CFUs per cubic meter.

Fall Winter Spring Summer

1231 384 2105 3175

1254 104 701 2526

1088 97 842 1090

1124    401 1243 1987

a) Examine the data using exploratory data analysis tools. Create at least one graph comparing means.

b) Perform an -way ANOVA to determine is the effect of the season is statistically significant. Use the four-step method. Be sure to give a practical conclusion. Assume the populations are normally distributed and the variances are roughly equal. Copy and paste the results of the test into your Word document.

Answer 1

Load the data into Excel.

Go to Data>Megastat.

Select the option Analysis of Variance and go to One Factor.

Select the data set for the Input Range.

Click OK.

The output obtained will be as follows:

	Mean	n	Std. Dev
	1,174.3	4	80.72	Fall
	246.5	4	168.75	Winter
	1,222.8	4	631.39	Spring
	2,194.5	4	882.09	Summer
	1,209.5	16	865.30	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	7,596,048.50	3	2,532,016.167	8.36	.0029
Error	3,635,195.50	12	302,932.958
Total	11,231,244.00	15
Post hoc analysis
p-values for pairwise t-tests
		Winter	Fall	Spring	Summer
		246.5	1,174.3	1,222.8	2,194.5
Winter	246.5
Fall	1,174.3	.0345
Spring	1,222.8	.0275	.9029
Summer	2,194.5	.0003	.0223	.0281
Tukey simultaneous comparison t-values (d.f. = 12)
		Winter	Fall	Spring	Summer
		246.5	1,174.3	1,222.8	2,194.5
Winter	246.5
Fall	1,174.3	2.38
Spring	1,222.8	2.51	0.12
Summer	2,194.5	5.01	2.62	2.50
critical values for experimentwise error rate:
		0.05	2.97
		0.01	3.89

a) Examine the data using exploratory data analysis tools. Create at least one graph comparing means.

The data from the output is:

Mean	n	Std. Dev
1,174.3	4	80.72	Fall
246.5	4	168.75	Winter
1,222.8	4	631.39	Spring
2,194.5	4	882.09	Summer
1,209.5	16	865.30	Total

The graph is as follows for the above data comparing means:

b) Perform an -way ANOVA to determine is the effect of the season is statistically significant. Use the four-step method. Be sure to give a practical conclusion. Assume the populations are normally distributed and the variances are roughly equal. Copy and paste the results of the test into your Word document.

The hypothesis of testing is:

Null hypothesis: The effect of the season is not statistically significant.

Alternative hypothesis: The effect of the season is statistically significant.

The ANOVA table from the output is:

ANOVA table
Source	SS	df	MS	F	p-value
Treatment	7,596,048.50	3	2,532,016.167	8.36	.0029
Error	3,635,195.50	12	302,932.958
Total	11,231,244.00	15

Since the p-value (0.0029) is less than the significance level, we can say that the effect of the season is statistically significant.

Or

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	7596049	3	2532016	8.358338	0.002865	3.490295
Within Groups	3635196	12	302933
Total	11231244	15

Decision & Conclusion:

Since F_calculated > F_critical, we can reject the null hypothesis and can say that the effect of the season is statistically significant.