Question

Four different types of insecticides are used on strawberry plants. The number of strawberries on each randomly selected plant is given below.

Insecticide 1	Insecticide 2	Insecticide 3	Insecticide 4
6	5	6	6
7	7	5	5
6	5	4	4
5	4	3	4
7	5	4	5
6	6	4	3

1. Does the data suggest that any of these insecticides yield a mean number of strawberries per plant that is different from the others? Use a 5% level of significance and be sure to verify the requirements for the test.

2. Construct side-by-side boxplots of the data resulting from each type of insecticide. Do they provide visual support for your decision in part a? Explain.   

(Hint: In StatCrunch under Other options: select Draw boxes horizontally. This will make the boxplots much easier to analyze.)

Use the P-value Approach for all hypothesis tests. Assume that all samples are randomly obtained.

Answer 1

b) Construct side-by-side boxplots of the data resulting from each type of insecticide. Do they provide visual support for your decision in part a? Explain.

From the above boxplot, we can observe that the area of insecticide 1 may be different from the insecticides 3 and 4 because the areas of the overlapping are small. But to know the exact significant requires a statistical test.

a) Does the data suggest that any of these insecticides yield a mean number of strawberries per plant that is different from the others? Use a 5% level of significance and be sure to verify the requirements for the test.

One-way ANOVA: strawberries versus Insecticide

Source	DF	SS	MS	F	P
Insecticide	3	12.833	4.278	4.50	0.014
Error	20	19.000	0.950
Total	23	31.833

S = 0.9747 R-Sq = 40.31% R-Sq(adj) = 31.36%

Comment: The estimated p-value for the one way ANOVA model is 0.014 and less than 0.05 significance level. Hence, we can conclude that at least one insecticide has a significant mean difference of strawberries from other insecticides at the 0.05 significance level.