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, 410 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: Number of Vines Checked (sample size) 410 400 Insecticide Pernod 5 Action Number of Infested Vines 40 23 At the 0.05 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

Answer 1

sal: Criven, ne: 400 mi - 410 X = 93 40 Xa = P = 0.0976 eos 0.0575 I the null and alternative hypothesis - Ho: P.-P2 - 0 Hi: P.-P270 Criven d= 0.05 The critical value is - 2012 - 1.96 Ho is rejected if Z <-1.96 ar Zy1.96 Paaled proportion p = XL + X2 nitna 63 810 = 0.0778 @ Test - statistic is - 7 = (f. - ) 10.0976 -0.0575 ) pc-P)(to + this) 0.0778 11-010778) (trot how Z 2.13 since, z = 2.13 > 1.96. So we reject the null hypothers.