Researchers at the National Cancer Institute released the results of a study tha

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 827 dogs from homes where an herbicide was used on a regular basis, diagnosing malignant lymphoma in 473 of them. Of the 130 dogs from homes where no herbicides were used, only 19 were found to have lymphoma. Test whether the weed-killing herbicides increases the chance of a dog being diagnosed with lymphoma. Use a significance level of 5%.

a. write null and alternative hypothesis

b. check all assumptions

c. find test statistic and p value

d. compare the p value to the significance level. what is your conclusion?

Explanation / Answer

a) Hypothesis:

Null hypothesis: P1 <= P2
Alternative hypothesis: P1 > P2

b)

independent random samples

c) Test statistic:

p1 = 473/827 = 0.578 , n 1 = 827 , p2 = 19/130 = 0.146, n2 = 130

p = (p1 * n1 + p2 * n2) / (n1 + n2)

= [(0.578 * 827) + (0.146 * 130)] / (827 + 130)

= 0.519

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = sqrt [ 0. 519 * 0.481 * ( 1/827 + 1/130 ) ]

= .047

z = (p1 - p2) / SE

= (0.578 - 0.146)/0.047

= 9.19

Now, we need to find p value using z = 9.19

p value =  0.00001.

d) As p value is less than the significance level. So, we reject the null hypothesis

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

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