Sampling Distribution of the Sample Proportion — Quiz
Question 3 • Math 4
Beet farmers claim that 76 percent of vegetarians like beets, while only 41 percent of carnivores like beets. Suppose a random samples of 21 vegetarians and 31 carnivores are asked if they like beets. Let hat p sub v and hat p sub c be the sample proportions of vegetarians and carnivores, respectively, who like beets. Which of the following is the correct shape and justification of the sampling distribution of hat p sub v minus hat p sub c ?
Answer
A
not approximately Normal because the expected numbers of successes and failures for the vegetarian group are not both at least 10
B
not approximately Normal because the expected numbers of successes and failures for each sample are all at least 10
C
bimodal because one population proportion is centered at 0 point 7 6 , while the other is centered at 0 point 4 1
D
approximately Normal because the expected numbers of successes and failures for each sample are all at least 10