Question

Directions: Use the P-value Approach for all hypothesis tests. Follow all the steps used in hypothesis testing as delineated in the Guided Notes or the textbook and be sure to verify the conditions for each test. Include any StatCrunch, SurfStat, graphing calculator, etc... output used in the process. I am assuming that all questions will be answered using technology-it is not necessary to include by-hand construction of the test statistics. Submitting test statistics only will not earn you full credit for that portion of the problem. Assume that all samples are randomly obtained Question #1: Four different types of insecticides are used on strawberry plants. The number of strawberries on each randomly selected plant is given below. InsecticideInsecticideInsecticide Insecticide 2 4 4 4 4 5 4 4 4 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. 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 (Hint: In StatCrunch under Other options: select Draw boxes horizontally. This will make the boxplots much easier to analyze.)

Answer 1

Answer:

MINITAB used

a).

Lavene's test , P=0.872 which is > 0.05 level shows that the normality assumption is not violated.

One-way ANOVA: Insecticide 1, Insecticide 2, Insecticide ... secticide 4

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Factor	4	Insecticide 1, Insecticide 2, Insecticide 3, Insecticide 4

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	3	12.83	4.2778	4.50	0.014
Error	20	19.00	0.9500
Total	23	31.83

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
0.974679	40.31%	31.36%	14.05%

Means

Factor	N	Mean	StDev	95% CI
Insecticide 1	6	6.167	0.753	(5.337, 6.997)
Insecticide 2	6	5.333	1.033	(4.503, 6.163)
Insecticide 3	6	4.333	1.033	(3.503, 5.163)
Insecticide 4	6	4.500	1.049	(3.670, 5.330)

Pooled StDev = 0.974679

Calculated F= 4.50, P=0.014 which is < 0.05 level of significance. Ho is rejected. We conclude that mean number of strawberries per plant that is different for the 4 insecticides.

b).

The box plot support the decision of part a.