Deck 11: Sampling Distributions and Normal Distributions

Question 1

The difference between a sample result and a census result is the

A) confidence line
B) margin of error
C) methodological artifact
D) sampling error

Answer 1

sampling error

Question 2

Which sampling distribution will typically have the smallest standard error?

A) a sampling distribution based on samples from a population with a variance of 5
B) a sampling distribution based on samples from a population with a variance of 25
C) a sampling distribution based on samples from a population with a variance of 90
D) a sampling distribution based on samples from a population with a variance of 100

Answer 2

a sampling distribution based on samples from a population with a variance of 5

Question 3

Which of the following sampling procedures will support inferential statistics?

A) convenience sampling
B) purposive sampling
C) quota sampling
D) simple random sampling

Answer 3

simple random sampling

Question 4

A researcher takes a sample of 500 NFL football fans. In the sample the average size of their largest home TV is 54 inches. Our researcher estimates the value of the standard error to be 3 inches. Complete the following statements: "I am 68 percent sure that the true average size for NFL football fans of their largest home TV is between __________ and __________."

A) 3 inches … 54 inches
B) 53 inches … 55 inches
C) 52 inches … 56 inches
D) 51 inches … 57 inches

Question 5

The center of a sampling distribution corresponds on the number to the

A) parameter value
B) sample size
C) sampling error
D) standard error

Question 6

Which of the following statements is correct?

A) As the sample size increases, the standard error decreases.
B) Standard errors of sampling distributions can be calculated from the results of non-probability samples.
C) Both "a" and "b" are correct.
D) None of the above is correct.

Question 7

A variable is normally distributed with a mean of 50, a standard deviation of 5, and a variance of 25. What is the value of its median?

A) 5
B) 25
C) 50
D) 100

Question 8

A researcher measured the pulse of a random sample of students finishing the SAT exam. The results of the study were sample size = 25, sample mean = 80, and sample standard deviation = 20. What is the best estimate for the standard error of the sampling distribution?

A) 3.2
B) 4
C) 5
D) 16

Question 9

If a researcher wants to make a statement with a 95% level of confidence, the margin of error is the standard error multiplied by

A) 1
B) 2
C) 3
D) 5

Question 10

One thousand researchers each take random samples of 1,000 Americans and ask their age. The sampling distribution has a standard error of 0.5 years. If the true average age of the population is 38, what percent of the researchers will get an average sample age between 36.5 and 39.5 years?

A) 38%
B) 68%
C) 95%
D) 99.7%

Question 11

Which of the following statements is correct?

A) As the standard error decreases, the margin of error increases.
B) Where the center of a sampling distribution occurs on the number line depends on the size of the samples being taken.
C) Both "a" and "b" are correct.
D) None of the above is correct.

Question 12

That sampling distributions based on large samples are normal distributions is proven by

A) the Central Limit Theorem
B) Gauss' Axiom
C) the Thomas Theorem
D) Zipf's Law

Question 13

Which of the following statements is correct?

A) As the standard error decreases, the margin of error decreases.
B) The larger the margin of error, the wider the confidence interval will be.
C) Both "a" and "b" are correct.
D) None of the above is correct.

Question 14

Which sampling distribution will typically have the smallest standard error?

A) a sampling distribution based on samples of size 50
B) a sampling distribution based on samples of size 150
C) a sampling distribution based on samples of size 500
D) a sampling distribution based on samples of size 1,500

Question 15

A _____ shows how frequently particular statistical results would occur if every possible sample of a particular size from a particular population were taken.

A) census distribution
B) frequency distribution
C) Poisson distribution
D) sampling distribution

Question 16

A sampling distribution has a mean of 100 and a standard error of 2. What percent of samples will get sample results between 98 and 102?

A) 2%
B) 4%
C) 68%
D) 95%

Question 17

A measure of dispersion for a sampling distribution is the

A) sampling frame
B) standard deviation
C) standard error
D) sampling interval

Question 18

Which sampling distribution will typically have the smallest standard error?

A) a sampling distribution based on cluster random sampling
B) a sampling distribution based on simple random sampling
C) a sampling distribution based on stratified random sampling
D) a sampling distribution based on systematic random sampling

Question 19

_____ are characteristics of populations; _____ are characteristics of samples.

A) parameters … statistics
B) pointers … values
C) statistics … parameters
D) values … pointers

Question 20

Which of the following statements is correct?

A) As the variation in the population decreases, the standard error decreases.
B) Researchers prefer to have a small standard error.
C) Both "a" and "b" are correct.
D) None of the above is correct.

Question 21

Why do researchers prefer sampling distributions with small standard errors?

Question 22

A researcher measured the pulse of a random sample of runners finishing the Boston Marathon. The results of the study were sample size = 100, sample mean = 160, and sample standard deviation = 20. What is the best estimate for the standard error of the sampling distribution? __________

Question 23

If scores on the SAT exam are normally distributed with a mean of 1000 and a standard deviation of 200, what percent of persons score

A) Above 1400? __________
B) Between 600 and 1200? __________
C) Below 800? __________
D) Is this problem about a frequency distribution or a sampling distribution? (frequency / sampling)

Question 24

A researcher takes a sample of 500 professional sociologists. In the sample the average annual income for the sociologists is $100,000. Our researcher estimates the value of the standard error to be $500. Complete the following statements:

A) The sample result was __________ with a margin of error of ___________ and a level of confidence of 95 percent.
B) I am 95 percent sure that the true average annual income for sociologists is between __________ and __________.

Question 25

What is the difference between a standard deviation and a standard error?

Question 26

What are confidence intervals, confidence levels, and margins of error?

Question 27

Which of the following statements is correct?

A) A probability sample will always give you a result within one standard error of the true value (census value) in the population.
B) Most variables are normally distributed in the population but very few sampling distributions are normal distributions.
C) Both "a" and "b" are correct.
D) None of the above is correct.

Question 28

One-thousand researchers each estimate the average number of CDs owned by students by asking 500 randomly-selected students. The distribution of results from the 1,000 samples has a mean of 100 CDs and a standard error of 3 CDs. Of the 1000 professors, what percent will probably get an estimate

A) Below 94 CDs? __________
B) Between 94 and 106 CDs? __________
C) Above 103 CDs? __________
D) Is this problem about a frequency distribution or a sampling distribution? (frequency / sampling)
E) What is the mode for this distribution? __________

Question 29

Which of the following statements is correct?

A) Researchers prefer to have a small standard error.
B) As the standard error increases, the width of the 95% confidence interval decreases.
C) Both "a" and "b" are correct.
D) None of the above is correct.

Question 30

What kinds of questions can you answer using the properties of sampling distributions and normal distributions?

Question 31

What are the properties of a normal distribution?

Question 32

What is the difference between a frequency distribution and a sampling distribution?

Question 33

The length of time presidents of universities stay in office is normally distributed with a mean of 5 years and a standard deviation of 2 years. What percent of university presidents stay in office

A) More than 9 years? __________
B) Less than 3 years? __________
C) Between 3 and 7 years? __________
D) Is this problem about a frequency distribution or a sampling distribution? (frequency / sampling)
E) What is the median number of years university presidents stay in office? __________

Question 34

A researcher takes a random sample from a population. What is the percent chance the sample result will be within two standard errors of the true value in the population?

A) 68%
B) 95%
C) 99.7%
D) 100%

Question 35

A researcher takes a sample of 500 executives in large U.S. corporations. In the sample the average annual income for the executives is $500,000. Our researcher estimates the value of the standard error to be $10,000. Complete the following statements: "The sample result was $500,000 with a margin of error of ___________ and a level of confidence of 95 percent."

A) $1,000
B) $10,000
C) $20,000
D) $480,000

Question 36

What does the central limit theorem say about sampling distributions?

Question 37

One-thousand professors each estimate the average number of books read last year by students by asking 500 randomly-selected students. The distribution of results from the 1,000 samples has a mean of 10 books and a standard error of 1 book. Of the 1000 professors, what percent will probably get an estimate

A) Above 12 books? __________
B) Between 10 and 12 books? __________
C) Below 10 books? __________
D) Is this problem about a frequency distribution or a sampling distribution? (frequency / sampling)

Question 38

A variable is normally distributed. Approximately what percent of cases have values within two standard deviations of the mean?

A) 50%
B) 68%
C) 95%
D) 99.7%

Question 39

What three things affect the size of the standard error?

Question 40

A researcher takes a sample of 500 employed college graduates and asks them how long it took them to find a job after college. In the sample the average length of time was 65 days. Our researcher estimates the value of the standard error to be 5 days. Complete the following statements:

A) The sample result was __________ with a margin of error of ___________ and a level of confidence of 68 percent.
B) I am 95 percent sure that the true average # of days to find a job after college is between __________ and __________.