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 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 was checked. The results are as follows:
Insecticide Number of Vines Checked
(Sample Size) Percent of
Infected Vines
Pernod 5 400 6%
Action 400 9%
a. 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?
Complete the following:
1. State H0.
2. State H1.
3. State the value of ?.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.
b. Suppose the sample sizes were both 600 instead of 400 and the percentages of infected plants in the samples remain the same for each type spray. Does that change the conclusion you reached in part (a)? How?
c. Discuss the effect that sample size had on the outcome of this analysis and, in general, on the effect sample size plays in hypothesis-testing.