The Damon family owns a large grape vineyard in western New Yorkalong Lake Erie. The grapevines must be sprayed at the beginning ofthe 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 andsprayed with Pernod 5, and three others were sprayed with Action.When the grapes ripened, 400 of the vines treated with Pernod 5were checked for infestation. Likewise, a sample of 380 vinessprayed with Action were checked. The results are:
| Insecticide | Number of Vines Checked (sample size) | Number of Infested Vines |
| Pernod 5 | 400 | 25 |
| Action | 380 | 42 |
|
At the 0.10 significance level, can we conclude that there is adifference in the proportion of vines infested using Pernod 5 asopposed to Action? Hint: For the calculations, assume thePernod 5 as the first sample.
State the decision rule. (Negative amounts should beindicated by a minus sign. Do not round the intermediate values.Round your answers to 2 decimal places.)
Compute the pooled proportion. (Do not round theintermediate values. Round your answer to 2 decimalplaces.)
Compute the value of the test statistic. (Negativeamount should be indicated by a minus sign. Do not round theintermediate values. Round your answer to 2 decimalplaces.)
What is your decision regarding the null hypothesis?
