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, 400 of the vines treated with Pernod 5 were checked for infestation. Like- wise, a sample of 400 vines sprayed with Action were checked. The results are: EXERCISES Republicans Democrats Number sampled 1,000 800 Number in favor 200 168 Number of Vines Checked Number of Insecticide (sample size) Infested Vines Pernod 5 400 24 Action 400 40 At the .05 significance level, can we conclude that there is a difference in the pro- portion of vines infested using Pernod 5 as opposed to Action

Answer 1

Please find the attached file of the complete question:

Explanation:

Given:

`Pernod \ 5: n_1= 400\\\\ p_1=(29)/(400)=0.0725\\\\Action: \ n_2= 400\\\\ p_2=(38)/(400)= 0.095\\\\`

Calculating the value of the test hypothesis:

`H_(O) \ :p_1-p_2=0\\\\ \ H_(a):p_1-p_2 \\eq 0`

Let
`a=0.02` is the critical value
`Z(0.01)= -2.33`

`H_0` rejects when
`z <-2.33 \ \ or\ \ z >2.33 .`

Calculating the Pooled proportion:

`= ((29+38))/((400+400))\\\\ = ((67))/((800)) \\\\ = 0.08375\\\\=0.084`