Question

The following questions require that you conduct appropriate tests of the null hypotheses outlined in each question using an =0.05 significance level. In all cases you are expected to use the appropriate inferential statistical test available in the Excel data analysis tool pack. Questions requiring a post hoc means comparison test (ie Scheffe’s or Tukey’s HSD test) are worth 20 marks, otherwise they are worth 10 marks.

A biologist is interested in the nutritional quality of different species of plants that make up the diet of caribou. For this, he has measured the concentration of protein in dried samples of each species. Test the null hypothesis that there is no difference in the protein content of the four plants. If necessary, complete a means comparison test (i.e. Scheffé's test). The data from this study are found on the Part III 3.1 worksheet.

Species 1	Species 2	Species 3	Species 4
431.1	444.6	385.5	366.8
441.2	472.8	386.9	369.8
442.2	446.7	362.4	382.6
454.3	451.8	391.4	351.4
448.6	454.4	399.1	377.2
450.2	458.9	401.7	376.4

Answer 1

The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃ = µ₄

H_a: At least one means is not equal

	Mean	n	Std. Dev
	444.60	6	8.259	Species 1
	454.87	6	10.194	Species 2
	387.83	6	14.036	Species 3
	370.70	6	10.999	Species 4
	414.50	24	38.131	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	30,990.173	3	10,330.0578	84.31	1.60E-11
Error	2,450.587	20	122.5293
Total	33,440.760	23

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference in the protein content of the four plants.

The means comparison test result is:

There is a significant main difference between Species 1 and Species 3.

There is a significant main difference between Species 1 and Species 4.

There is a significant main difference between Species 2 and Species 3.

There is a significant main difference between Species 2 and Species 4.