The Damon family owns a large grape vineyard in the Niagara Peninsula. The grapevines must be sprayed at the beginning of the growing season to protect them against various insects and diseases. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, six long rows were selected. Three rows were sprayed with Pernod 5 and three 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 was checked. The results are: Insecticide Pernod 5 Action Number of Vines Checked (sample size) 400 400 Number of Infested Vines 29 38 Can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action? Test at the 0.05 significance level. Determine and interpret the p-value. a. State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answers to 2 decimal places.) Ho is rejected if z< or z>O b. Compute the pooled proportion. (Round the final answer to 2 decimal places.) Pooled proportion c. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the intermediate calculations and final answer to 2 decimal places.)
The Damon family owns a large grape vineyard in the Niagara Peninsula. The grapevines must be sprayed at the beginning of the growing season to protect them against various insects and diseases. Two new insecticides have just been marketed: Pernod 5 and Action. To test their effectiveness, six long rows were selected. Three rows were sprayed with Pernod 5 and three 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 was checked. The results are: Insecticide Pernod 5 Action Number of Vines Checked (sample size) 400 400 Number of Infested Vines 29 38 Can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action? Test at the 0.05 significance level. Determine and interpret the p-value. a. State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answers to 2 decimal places.) Ho is rejected if z< or z>O b. Compute the pooled proportion. (Round the final answer to 2 decimal places.) Pooled proportion c. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the intermediate calculations and final answer to 2 decimal places.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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Transcribed Image Text:The Damon family owns a large grape vineyard in the Niagara Peninsula. The grapevines must be sprayed at the beginning of the
growing season to protect them against various insects and diseases. Two new insecticides have just been marketed: Pernod 5 and
Action. To test their effectiveness, six long rows were selected. Three rows were sprayed with Pernod 5 and three 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 was checked. The results are:
Insecticide
Pernod 5
Number of Vines Checked
(sample size)
400
Number of
Infested Vines
29
Action
400
38
Can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action? Test at the 0.05
significance level. Determine and interpret the p-value.
a. State the decision rule. (Negative answer should be indicated by a minus sign. Round the final answers to 2 decimal places.)
Ho is rejected if z <[
or z>
b. Compute the pooled proportion. (Round the final answer to 2 decimal places.)
Pooled proportion
c. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the intermediate
calculations and final answer to 2 decimal places.)
Value of the test statistic
d. What is your decision regarding the null hypothesis?
Ho is not rejected
e. Determine the p-value. (Round the z-value to 2 decimal places. Round the final answer to 4 decimal places.)
The pvalue is
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