Question: The Damon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginning of the growing season to protect against various insects and diseases. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, three long rows were selected and sprayed with Pernod 5, and three others were sprayed with Action. When the grapes ripened, 400 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 400 vines sprayed with Action were checked. The results were:

Insecticide Number vines checked (sample size) Number of infested vines
Pernod 5 400 24
Action 400 40

At the .05 level of significance, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action?

This is a two-sample test involving proportions instead of means.

Required:

? Is there any difference in sampling theory as it applies to tests of sample means vs. tests of sample proportions? Discuss.

? Show all 5 steps to test the above problem.

? Spend time on your conclusion -- state whether you reject the null or you do not reject it (fail to reject) and then discuss what this conclusion means as it relates to this particular problem.