Question

A vetinarian is investigating a particular disease of cows. She is interested in whether English cows differ from Scottish cows in their probability of suffering from this particular disease. A sample of 62 cows is taken, of which 30 are English and 32 are Scottish. It is not known if English cows are more or less likely to have this disease. In the sample, there are 15 healthy cows, of which 3 are English.

state

country healthy diseased

England 3 27

Scotland 12 20

Estimate the probability of: (a), an English, and (b), a Scottish cow, having the disease; give a 95% confidence interval (you may use the normal approximation)

Answer 1

(a) Probability of English cow having disease = 3/27 = 0.1111

95% confidence interval for proportion of English cows having disease

For 95% confidence interval , critical value of z is

zc = 1.96 ( from z table)

Thus , 95% confidence interval for proportion of English cows having disease

= ( -0.0074 , 0.2297)

(b) Probability of Scottish cow having disease = 12/32 = 0.375

95% confidence interval for proportion of Scottish cows having disease

For 95% confidence interval , critical value of z is

zc = 1.96 ( from z table)

Thus , 95% confidence interval for proportion of Scottish cows having disease

= (0.2073 , 0.5427 )