Question

Rhagoletis pomonella, the apple maggoty, is a serious pest on commercial apples both in New York and Washington State. It is thought that R. pomonella fed on hawthorn until apples were introduced into the U.S. during the nineteenth century. This insect then moved to apples and has remained a control problem in commercial orchards ever since. An entomologist trying to develop elective and environmentally safe control measures for R. pomonella tested the following baits in standard traps.

A: protein bait alone

B: protein bait plus 10% ammonium carbonate

C: protein bait plus 10% ammonium acetate

D: 10 g ammonium acetate alone

1. Test the hypothesis showing all steps

2. Analyze with one-way ANOVA to test the hypothesis that there is any significant differences between the three type of treatments at both: 95% level of significance and 90% level of significance

3: Would a post hoc test be necessary at both 95% level of significance and 90% level of significance?

	Treatment
	A	B	C	D
	131	152	205	201
	150	165	230	185
	175	149	200	175
	143	181	195	206
Mean	149.8	161.8	207.5	191.8

Answer 1

A good knowledge on the concept of ANOVA and the calculations necessary for testing the hypothesis of equality in treatment means is necessary as a prerequisite to understand the solution to the problem given. Another point I want to note, here the level of significance on which the testing on which ANOVA is told to be performed is a bit higher than what we actually. It could have been 95% and 90% confidence level and 5% and 10% level of significance in case it is mentioned wrong, since we generally do not take the levels of significance as so high. But even in this case too, the p-value obtained in ANOVA is less than all the levels of significance that might be happening, i.e., 5%, 10%, 90% and 95% levels of significance. Our p-value is something of the order 10^-6 so it is less than all of them. The Solution is given below: