1. A simple random sample of 120 vet clinics in the Midwest reveals that the vas

Question

1. A simple random sample of 120 vet clinics in the Midwest reveals that the vast majority of them only treat small pets (dogs, cats, rabbits, etc.) and no large animals (cows, horses, etc.). Of the 120 clinics sample d, 88 responded that they do not treat large animals at their clinic.

a. What is a 90% confidence interval for p , the population proportion of vet clinics that do treat large animals? Tell whether the population proportion of vet clinics that do treat large animals is above 25%. Why?

b. If a 95% confidence interval were calculated instead, what would happen to the width of the confidence interval? Why?

Explanation / Answer

a) point estimate p=(120-88)/120=0.267

for std error =(p[(1-p)/n)1/2 =0.0404

for 90% CI, z=1.645

hence confidence interval =point estimate -/+ z*std error =0.2003 ; 0.3331

as above interval contains value below 0.25 also ; we can not conclude that  population proportion of vet clinics that do treat large animals is above 25%..

b) for 95% confidence interval has higher value of z score ; the width will increase

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