Question

Researchers at the national cancer institute released the results of a study that investigated the effect of weed-killing herbicides on house pets. they examined 800 cats from homes where a herbicide was used on a regular basis, diagnosing malignant lymphoma in 390 of them. of the 200 cats from homes where no herbicides were used, 39 were found to have lymphoma.

a.) construct a 99% confidence interval for this difference

b.) state an appropriate conclusion

Answer 1

Let p1 denote proportion of cats having lymphoma from home where herbicides were used and p2 denote proportion of cats having lymphoma from home where herbicides were not used.

99% confidence interval is

(p1-p2) -+ 2.576* sqrt( p1(1-p1)/n1 + p2(1-p2)/n2)

(0.487-0.195) -+ 2.576*sqrt(0.487*0.513/800 + 0.195*0.805/200)

0.292 -+ 2.576*sqrt(0.0003+ 0.00078)

0.292 -+ 2.576*0.032

0.292 -+ 0.082

( 0.21 , 0.374)

Since interval does not contain 0 and is greater than 0.Thus proportion of cats having lymphoma from home where herbicides were used is greater than those where herbicides were not used.