Sampling Distribution of the Sample Proportion — Quiz
Question 7 • Math 4
Movie critics claim that 68 percent of adults and 79 percent of teenagers would recommend seeing the newest action movie. Suppose random samples of 43 adults and 52 teenagers are selected. Let hat p sub cap A and hat p sub cap t be the sample proportions of adult and teenage moviegoers, respectively, who would recommend this movie. Which of the following is the correct shape and justification of the sampling distribution of hat p sub cap A minus hat p sub cap t ?
Answer
A
approximately Normal because the expected numbers of successes and failures for each sample are all at least 10
B
not approximately Normal because the expected numbers of successes and failures for the adult group are not both at least 10
C
not approximately Normal because the expected numbers of successes and failures for each sample are all at least 10
D
bimodal because one population proportion is centered at 0 point 6 8 , while the other is centered at 0 point 7 9