AnswersMath 4Sampling Distribution of the Sample Proportion

Sampling Distribution of the Sample Proportion — Quiz Answers

10 verified answers
3

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 ?

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
4

The proportion of twins born in a town is p is equal to 0 point 1 2 Suppose we randomly select 100 women from this town who give birth in the next year. Which of the following is the mean of the sampling distribution of hat p ?

A
mu sub hat p is equal to n p is equal to 100 times 0 point 1 2 is equal to 12
B
mu sub hat p is equal to p is equal to 0 point 1 2
C
mu sub hat p is equal to 1 minus p is equal to 1 minus 0 point 1 2 is equal to 0 point 8 8
D
mu sub hat p is equal to n times open paren 1 minus p close paren is equal to 100 times open paren 1 minus 0 point 1 2 close paren is equal to 88
5

Movie critics claim that 68 percent of adults and 79 percent of teenagers would recommend seeing the newest action movie. Suppose a random sample of 43 adults and 52 teenagers is 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 calculation and interpretation of the standard deviation of the sampling distribution of hat p sub cap A minus hat p sub cap t ?

A
The difference (adult – teenager) in the sample proportions of those who would recommend this action movie varies about 0 point 0 4 3 from the true difference in proportions.
B
The difference (adult – teenager) in the sample proportions of those who would recommend this action movie varies about 0 point 1 7 6 from the true difference in proportions.
C
The difference (adult – teenager) in the sample proportions of those who would recommend this action movie varies about 0 point 0 0 8 from the true difference in proportions.
D
The difference (adult – teenager) in the sample proportions of those who would recommend this action movie varies about 0 point 0 9 1 from the true difference in proportions.
7

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 ?

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
8

A professional tennis player has a serve-return rate of p is equal to 0 point 7 1 A random sample of 55 serve returns is selected. Which of the following is the mean of the sampling distribution of hat p ?

A
mu sub hat p is equal to n times open paren 1 minus p close paren is equal to 55 times open paren 1 minus 0 point 7 1 close paren is equal to 15 point 9 5
B
mu sub hat p is equal to n p is equal to 55 times 0 point 7 1 is equal to 39 point 0 5
C
mu sub hat p is equal to p is equal to 0 point 7 1
D
mu sub hat p is equal to 1 minus p is equal to 1 minus 0 point 7 1 is equal to 0 point 2 9
9

A professional tennis player has a serve-return rate of p is equal to 0 point 7 1 A random sample of 55 serve returns is selected. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of hat p ?

A
sigma sub hat p is equal to 0 point 0 0 4 . In SRSs of size 55 , the sample proportion of this tennis player’s serve-return rate typically varies 0 point 0 0 4 from the true proportion p is equal to 0 point 7 1 .
B
sigma sub hat p is equal to 0 point 1 1 4 . In SRSs of size 55 , the sample proportion of this tennis player’s serve-return rate typically varies 0 point 1 1 4 from the true proportion p is equal to 0 point 7 1 .
C
sigma sub hat p is equal to 0 point 0 6 1 . In SRSs of size 55 , the sample proportion of this tennis player’s serve-return rate typically varies 0 point 0 6 1 from the true proportion p is equal to 0 point 7 1 .
D
sigma sub hat p is equal to 0 point 0 1 3 . In SRSs of size 55 , the sample proportion of this tennis player’s serve-return rate typically varies 0 point 0 1 3 from the true proportion p is equal to 0 point 7 1 .
10

The proportion of twins born in a town is p is equal to 0 point 1 2 Suppose we randomly select 100 women from this town who give birth in the next year. Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of hat p ?

A
σp^=0.106. In SRSs of size 100 , the sample proportion of women in this town giving birth to twins typically varies 0 point 1 0 6 from the true proportion, p is equal to 0 point 1 2 .
B
σp^=0.001. In SRSs of size 100 , the sample proportion of women in this town giving birth to twins typically varies 0 point 0 0 1 from the true proportion, p is equal to 0 point 1 2 .
C
σp^=0.032. In SRSs of size 100 , the sample proportion of women in this town giving birth to twins typically varies 0 point 0 3 2 from the true proportion, p is equal to 0 point 1 2 .
D
σp^=0.035. In SRSs of size 100 , the sample proportion of women in this town giving birth to twins typically varies 0 point 0 3 5 from the true proportion, p is equal to 0 point 1 2 .

Did you find these answers helpful?

Sampling Distribution of the Sample Proportion…