Chapter 18: Sam pling Distribution M odels

Stats: Modeling the World - Bock, Velleman, & DeVeaux
parameter
statistic
proportion
sampling distribution
model
Central Limit Theorem
Standard error
1. Explain the difference between a parameter and a statistic.
2. Explain the difference between p and pˆ ?
3. What is meant by sampling variability?
4. What is meant by the sampling distribution model of a statistic?
5. How is the size of a sample related to the spread of the sampling distribution?
6. In an SRS of size n, what is true about the sampling distribution of pˆ when the sample size n
increases?
7. In an SRS of size n, what is the mean of the sampling distribution of pˆ ?
8. In an SRS of size n, what is the standard deviation of the sampling distribution of pˆ ?
Chapter 18: Sampling Distribution Models
Stats: Modeling the World - Bock, Velleman, & DeVeaux
9. What happens to the standard deviation of pˆ as the sample size n increases?
10. When does the formula
pq
apply to the standard deviation of pˆ ?
n
11. When the sample size n is large, the sampling distribution of pˆ is approximately normal.
What test can you use to determine if the sample is large enough to assume that the sampling
distribution is approximately normal?
12. The mean and standard deviation of a population are parameters.
What symbols are used to represent these parameters?
13. The mean and standard deviation of a sample are statistics.
What symbols are used to represent these statistics?
14. Because averages are less variable than individual outcomes, what is true about the standard
deviation of the sampling distribution of x ?
15. What is the mean of the sampling distribution of x , if x is the mean of an SRS of size n
drawn from a large population with mean µ and standard deviation σ?
16. What is the standard deviation of the sampling distribution of x , if x is the mean of an SRS
of size n drawn from a large population with mean µ and standard deviation σ?
Chapter 18: Sampling Distribution Models
Stats: Modeling the World - Bock, Velleman, & DeVeaux
17. To cut the standard deviation of x in half, you must take a sample _____ times as large.
18. When should you use
σ
n
to calculate the standard deviation of x ?
19. If σ is not known, what can you use to estimate the standard deviation of x ? What is this
called?
20. What does the central limit theorem say about the shape of the sampling distribution of x ?
21. What does the law of large numbers state?
Chapter 18: Sampling Distribution Models