Question

The American Veterinary Medical Association conducted a survey of veterinary clinics to estimate the proportion that do not treat large animals (cows, horses, etc.). The survey was mailed to a random sample of 120 veterinary clinics throughout the country and of these, 88 responded that they do not treat large animals. (a) (2 points) Calculate a 95% confidence interval for the population proportion p of veterinary clinics that do not treat large animals. (b) (5 points) Typically, 70% of the veterinary clinics in the world do not treat large animals. Use a hypothesis test to test whether American veterinary clinics are more likely not to provide this service. Use significance level α = 0.05.

Answer 1

Part a)

n = 120



Lower Limit =
upper Limit =
95% Confidence interval is ( 0.6542 , 0.8124 )
( 0.6542 < P < 0.8124 )

Part b)

To Test :-

H0 :- P = 0.70

H1 :- P > 0.70

n = 120
P = X / n = 0.7333

Test Statistic :-


Z = 0.8

Test Criteria :-
Reject null hypothesis if

= 0.8 < 1.645, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z > 0.8 )
P value = 0.2119
Reject null hypothesis if P value <
Since P value = 0.2119 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to support the claim that American veterinary clinics are more likely not to provide this service.