Question

In: Statistics and Probability

The Sander’s family owns a large grape vineyard in Jackson, Mississippi. The grape vines must be...

The Sander’s family owns a large grape vineyard in Jackson, Mississippi. The grape vines 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 other 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:
Number of
Vines Checked Number of
Insecticide (sample size) Infested Vines
Pernod 5 400 24
Action 400 40​
At the .04 significance level, can we conclude that there is a difference in the proportion of the vines infested using Pernod 5 as opposed to Action?

please show all steps and work.

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