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, 440 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 360 vines sprayed with Action were checked. The results are:

Insecticide	Number of Vines Checked (sample size)	Number of Infested Vines
Pernod 5	440	36
Action	360	30

At the 0.05 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.

2. Compute the pooled proportion

3. Compute the value of the test statistic

4. What is your decision regarding the null hypothesis?

Reject

Fail to reject

Answer 1

Given:

The Damon family owns a large grape vineyard in western New York along Lake Erie.

When the grapes ripened, 440 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 360 vines sprayed with Action were checked. The results are:

Insecticide	Number of Vines Checked (sample size)	Number of Infested Vines
Pernod 5	440	36
Action	360	30

X1 = 36 n1 = 440

X2 = 30 n2 = 360

Hypothesis test:

The null and alternative hypothesis is

Ho : p1 = p2

Ha : P1 p2

At 0.05 significance level the critical value of Z is

Z/2 = Z0.05/2 = 1.96

1) Dicision rule :

Reject Ho, if Z > 1.96 or Z < -1.96 otherwise fail to reject.

Fail to reject the null hypothesis.

At the 0.05 significance level, we can not conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action.