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, 390 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 420 vines sprayed with Action were checked. The results are: Number of Infested Vines Insecticide Pernod 5 Action Number of Vines Checked (sample size) 390 420 66 At the 0.10 significance level, can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action? Hint. For the calculations, assume the Pernod 5 as the first sample. 1. State the decision rule. (Negative amounts should be indicated by a minus sign. Do not round the intermediate values. Round your answers to 2 decimal places.) HO is rejected if z< or Z b. Compute the pooled proportion. (Do not round the intermediate values. Round your answer to 2 decimal places.) Pooled proportion C. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Do not round the intermediate values. Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding the null hypothesis?

Answer 1

390 Pernods - (P.) sample proportion = = 47 2041205 Action - (P22 Sample proportion Parte 66 20.1571 intto: b = P2 Versus Ha: Piala (117 at 2=0.10 Significance lend 1 Hois Relejected it 22 [1.648 or 2>11.645 1.65 the test statistic 2 = 1 1 1 (0-1205-0157D 10.12088 0.8795+ V 0.1571X0.8429 420 390 ② Decision fail to reject to. There is no sufficient that kif evidence for two prom clains different