Question

1. The American Veterinary Medical Association (AMVA) 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 194 veterinary clinics throughout the country and of these, 148 responded that they do not treat large animals. Give a 95% confidence interval for the proportion of all vet clinics that do not treat large animals.  [6 points]

Make sure to include each of the following for full credit

1. State the estimate from the sample
2. State the margin of error
3. Write a sentence explaining your result in context

Answer 1

Solution :

Given that,

a) Point estimate = sample proportion = = x / n = 148 / 194 = 0.763

1 - = 1 - 0.763 = 0.237

Z/2 = Z0.025 = 1.96  

b) Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.763 * 0.237) / 194)

= 0.060

c) A 95% confidence interval for population proportion p is ,

± E  

= 0.763 ± 0.060

= ( 0.703, 0.823 )

We are 95% confident that the true proportion  of all vet clinics that do not treat large animals is between 0.703 and 0.823.