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

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. Likewise, a sample of 400 vines sprayed with Action were checked. The results are:

At the .10 significance level can we conclude that there is a difference is proportion of vines infested using pernod 5 as opposed to action . For the calculations assume pernod 5 is the sample.

1. state the decision rule (dont round intermediate values, final answer 2 decimals)

H0 is rejected if z<____ or z>____.

b. compute the pooled proportion (dont round intermediate values, final answer 2 decimals)

c.compute the value of the test statistic (dont round intermediate values, final answer 2 decimals)

d. what is your decision regarding the null hypotheses?

reject/do not reject

Explanation / Answer

Solution -

Pernod 5:

n1= 400

p1=29/400=0.0725

Action: n2= 400

p2=38/400= 0.095

From above value

Given a=0.02, the critical value is Z(0.01)= -2.33
H0 is rejected

if z <-2.33 or z >2.33 .

The test hypothesis is
Ho:p1-p2=0
Ha:p1-p2 not equal to 0

Pooled proportion= (29+38)/(400+400)=0.084

The test statistic we know that

Z=(p1-p2)/?[p*(1-p)*(1/400 + 1/400)]

=(0.0725-0.095)/sqrt(0.084*(1-0.084)*2/400)

= -1.15

3.The p-value is

2*P(Z<-1.15)= 0.2501

p-value is larger than a=0.02,

here we do not reject Ho

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