At a local veterinary office, 48% of dogs get their teeth cleaned, while 35% of cats get their teeth cleaned. Let and be the sample proportions of dogs and cats at this veterinary office, respectively, who get their teeth cleaned. Suppose 25 dogs and 32 cats from this veterinary office are selected at random to collect data on their teeth-cleaning history. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ? The difference (dogs – cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.003 from the true difference in proportions. The difference (dogs – cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.017 from the true difference in proportions. The difference (dogs – cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.054 from the true difference in proportions. The difference (dogs – cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.131 from the true difference in proportions.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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At a local veterinary office, 48% of dogs get their teeth cleaned, while 35% of cats get their teeth cleaned. Let  and  be the sample proportions of dogs and cats at this veterinary office, respectively, who get their teeth cleaned. Suppose 25 dogs and 32 cats from this veterinary office are selected at random to collect data on their teeth-cleaning history.

Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of  ?

The difference (dogs – cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.003 from the true difference in proportions.
The difference (dogs – cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.017 from the true difference in proportions.
The difference (dogs – cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.054 from the true difference in proportions.
The difference (dogs – cats) in the sample proportions of those that get their teeth cleaned typically varies about 0.131 from the true difference in proportions.
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