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

Number of vines checked:(Sample size)

Insecticide:                                                             Number of Infested Vines
Pernod 5                                     425                                        40

Action                               410                                        26

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? Assume the Pernod 5 as the first sample.

A.) 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.)

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

C.) 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.)

Answer 1

Given:

n1=425, X1=40, n2=410, X2=26, = 0.01

a)

ANSWER:  E.

Ho: P1 = P2

Ha: P1 P2

Calculation:

A)

Decision Rule:

Reject Ho, If |Z| > Z

Where,

Z/2 = Z 0.01/2 = 2.58        ...............Using standard Normal table

b) Pooled proportion:

Q = 1-P = 1-0.08 = 0.92

C)

Test statistic:

Conclusion:

|Z| < Z/2, i.e. 1.64 < 2.58, That is Fail to Reject Ho at 1% level of signfiicance.

Therefore, we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action .