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.

Boxplot of strawberries 4 4 Insecticide

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.