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, 425 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 410 vines sprayed with Action were checked. The results are:

Insecticide	Number of Vines Checked (sample size)	Number of Infested Vines
Pernod 5	425	42
Action	410	32

At the 0.02 significance level, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action? Hint: For the calculations, assume the Pernod 5 as the first sample.

1. State the decision rule.

H0 is rejected if z < _____ or z > ______.

2. Compute the pooled proportion.

3. Compute the value of the test statistic.

Answer 1

1:

H0 is rejected if z < -2.33 or z > 2.33.

2. Compute the pooled proportion.

p = 0.0886

3. Compute the value of the test statistic.

z = 1.06

Conclusion:

At the 0.02 significance level, we cannot conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action.