Question

2. A botanist developed a new fungicidal treatment to protect tomato plants from the fungal disease fusarium wilt. A study was conducted to assess its effectiveness. On each plant, two branches were randomly selected. The experimental fungicide (treatment) was sprayed on one of the two branches. The other branch was sprayed with a control, which is identical to the treatment spray- with the exception of the active ingredient. The selected branches of the plant were then exposed to the fungus. The outcomes for each branch are recorded as either infected or not infected for each of the two treatments. The results are summarized in the table below. Treatment Not Infected Infected Infected 560 286 Control Not Infected po a. Do these proportions represent matched-pairs data? b. Compute the sample test statistic. c. Does the evidence suggest that the new treatment has a different proportion of successes than the control? Use the a = 0.05 level of significance.

Answer 1

Answov: Given data- Treatment Infected Not infected TOLL Total Infected 560 286 846 Not Infected 156 83 239 716 Total 1085 369 No. of plants in treatment ni = 1085 No. of Plants in contool na -1085 No.of plants are not infected in treatment 24,=369 No. of plants are not infected in control X = 239 : Prorostions of not infected in treatment p=369 1085 P1034 propoblians of not infected in control P₂ 239 1085 P2 = 0.22

P = 2, +22 ritha 239 +369 1085+085 Jp = 0.28 :. Q = 1- = 1-0.18 To = 0.72 Hypothesis: The null and alternative Hypotheses are Hoi pi=P2 HI: PIEP2 Level of the significance is 0.05 . Test Statistics: unda Ho, the test statistic us defined as Za [P-ez]

10.34-0.22) Z = [0.28x0.72 (108s + ies) z = 6.217 | coitical value is Level of 5:9nificone is 0.05 so, coitical value of zis 1.96.