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, 430 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 350 vines sprayed with Action were checked. The results are:

Insecticide	Number of Vines Checked (sample size)	Number of Infested Vines
Pernod 5	430	26
Action	350	40

At the 0.01 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.

State the decision rule. (Negative amounts should be indicated by a minus sign. Do not round the intermediate values. Round your answers to 2 decimal places.)

Compute the pooled proportion. (Do not round the intermediate values. Round your answer to 2 decimal places.)

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Do not round the intermediate values. Round your answer to 2 decimal places.)

What is your decision regarding the null hypothesis?

Reject

Fail to reject

Answer 1

(a)

= 0.01

From Table, citical values of Z = 2.576

Decision Rule:
Reject Null Hypothesis if

Z_STAT < - 2.58

OR

Z_{STAT > 2.58}

(b)

So,

Pooled Proportion = 0.08

(c)

Q = 1 - P = 0.9154

So,

p1 = 26/430 = 0.0605

p2 = 40/350 = 0.1143

Test statistic is:

Z = (0.0605 - 0.1143)/0.0201 = - 2.68

So,

Test statistic is:

Z = - 2.68

(d)

Since calculated value of Z = - 2.68 is less than critical value of Z = - 2.58, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that there is difference between in the proportion of vines infested using Pernod 5 as opposed to Action.

So,

Correct option:

Reject