The Damon family owns a large grape vineyard in the Niagara Peninsula. The grape

Question

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, 300 of the vines treated with Pernod 5 were checked for infestation. Likewise, a sample of 300 vines sprayed with Action was checked. The results are: Can we conclude that there is a difference in the proportion of vines infested using Pernod 5 as opposed to Action? Test at the 0.01 significance level. Determine and interpret the p-value. a. State the decision rule. H_0 is rejected if z . b. Compute the pooled proportion. Pooled proportion 0.11 c. Compute the value of the test statistic. Value of the test statistic -1.98 d. What is your decision regarding the null hypothesis? H_0 is not rejected. e. Determine the p-value. The p-value is 0.0478.

Explanation / Answer

PArtA-

As we want to test for difference so test is two tailed and for alpha=0.01 critical values are -2.58 and +2.58

H0 is rejected if z<-2.58 ot z>2.58

Part-b

Proportion of vine infested using Pernord 5 is p1=26/326=0.08

Proportion of vine infested using Action is p2=40/340 =0.12

Pooled proportion p=(26+40)/(326+340)=0.10

Part-c

Test statistic Z=(p1-p2)/sqrt(p*(1-p)*(1/n1+1/n2))

=(0.08-0.12)/sqrt(0.10*(1-0.10)*(1/326+1/340))

=-1.72

Part-d

As calculated z>-2.58, we do not reject H0

Part-e

p-value=2*P(Z<-1.72)=0.0854 using excel function =2*NORMSDIST(-1.72)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.