1|Page
Emory University QTM 100 LE12 Lab 8: Exploring
Inferential Statistics & Sampling Distributions Newest Exam
Preparation With Complete Questions And Correct Answers
With Rationales Already Graded A+ Brand New Version!!
1. In inferential statistics, the primary purpose of a sampling
distribution is to:
A) Describe the spread of the original raw data.
B) Provide a probability distribution of a statistic computed from
repeated samples of the same size from the same population.
C) Replace the need for hypothesis testing by offering exact population
parameters.
D) Summarize the causal relationship between two variables.
Answer: B
Explanation: A sampling distribution is the distribution of a sample
statistic (e.g., mean, proportion) over many random samples of
identical size from the same population. Option A describes the data
distribution, C is incorrect because sampling distributions are used for
inference, not to replace tests, and D refers to regression or
experimental design.
,2|Page
2. The standard deviation of the sampling distribution of the sample
mean is called:
A) The population standard deviation.
B) The sample variance.
C) The standard error of the mean.
D) The margin of error.
Answer: C
Explanation: The standard error of the mean is specifically the standard
deviation of the sampling distribution of x-bar. It equals sigma / sqrt(n).
Option A is the population parameter, B is a sample-based measure,
and D is a multiplier times the standard error in confidence intervals.
3. According to the Central Limit Theorem, the sampling distribution of
the sample mean approaches a normal distribution as:
A) The population size increases.
B) The sample size increases, regardless of the population distribution
shape.
C) The population variance decreases to zero.
D) The sample standard deviation becomes equal to the population
standard deviation.
Answer: B
Explanation: The Central Limit Theorem states that for sufficiently large
sample sizes (typically n >= 30), the distribution of the sample mean will
be approximately normal, irrespective of the original population
distribution shape, provided the population has finite variance. Option A
,3|Page
is incorrect because the theorem concerns sample size, not population
size.
4. If a population is exactly normally distributed with mean 50 and
standard deviation 10, what is the mean of the sampling distribution of
the sample mean for samples of size 25?
A) 10
B) 50
C) 2
D) Cannot be determined without the sample data.
Answer: B
Explanation: The mean of the sampling distribution of the sample mean
equals the population mean, mu, regardless of sample size. Here mu =
50. Option A is the population standard deviation, C is the standard
error (10/sqrt(25)=2), and D is incorrect because we have the
population parameters.
5. For a sample size of 100, the standard error of the sample mean is 3.
If the sample size is increased to 400, what is the new standard error,
assuming population standard deviation remains constant?
A) 3
B) 6
C) 1.5
D) 0.75
Answer: C
, 4|Page
Explanation: Standard error = sigma/sqrt(n). If n quadruples from 100 to
400, sqrt(n) doubles, so the standard error is halved. = 1.5. Option
A is unchanged, B is doubled, D is quartered.
6. The law of large numbers states that:
A) As the sample size grows, the sample mean converges to the
population mean.
B) As the sample size grows, the sampling distribution becomes
perfectly normal.
C) Larger samples always eliminate bias.
D) The population variance decreases as sample size increases.
Answer: A
Explanation: The law of large numbers indicates that the sample
average approaches the expected value (population mean) as n
increases. Option B is the CLT, C is false because bias is a design issue, D
is false because population variance is fixed.
7. Which of the following is a parameter?
A) Sample proportion p-hat
B) Sample mean x-bar
C) Population standard deviation sigma
D) Sample standard deviation s
Answer: C
Emory University QTM 100 LE12 Lab 8: Exploring
Inferential Statistics & Sampling Distributions Newest Exam
Preparation With Complete Questions And Correct Answers
With Rationales Already Graded A+ Brand New Version!!
1. In inferential statistics, the primary purpose of a sampling
distribution is to:
A) Describe the spread of the original raw data.
B) Provide a probability distribution of a statistic computed from
repeated samples of the same size from the same population.
C) Replace the need for hypothesis testing by offering exact population
parameters.
D) Summarize the causal relationship between two variables.
Answer: B
Explanation: A sampling distribution is the distribution of a sample
statistic (e.g., mean, proportion) over many random samples of
identical size from the same population. Option A describes the data
distribution, C is incorrect because sampling distributions are used for
inference, not to replace tests, and D refers to regression or
experimental design.
,2|Page
2. The standard deviation of the sampling distribution of the sample
mean is called:
A) The population standard deviation.
B) The sample variance.
C) The standard error of the mean.
D) The margin of error.
Answer: C
Explanation: The standard error of the mean is specifically the standard
deviation of the sampling distribution of x-bar. It equals sigma / sqrt(n).
Option A is the population parameter, B is a sample-based measure,
and D is a multiplier times the standard error in confidence intervals.
3. According to the Central Limit Theorem, the sampling distribution of
the sample mean approaches a normal distribution as:
A) The population size increases.
B) The sample size increases, regardless of the population distribution
shape.
C) The population variance decreases to zero.
D) The sample standard deviation becomes equal to the population
standard deviation.
Answer: B
Explanation: The Central Limit Theorem states that for sufficiently large
sample sizes (typically n >= 30), the distribution of the sample mean will
be approximately normal, irrespective of the original population
distribution shape, provided the population has finite variance. Option A
,3|Page
is incorrect because the theorem concerns sample size, not population
size.
4. If a population is exactly normally distributed with mean 50 and
standard deviation 10, what is the mean of the sampling distribution of
the sample mean for samples of size 25?
A) 10
B) 50
C) 2
D) Cannot be determined without the sample data.
Answer: B
Explanation: The mean of the sampling distribution of the sample mean
equals the population mean, mu, regardless of sample size. Here mu =
50. Option A is the population standard deviation, C is the standard
error (10/sqrt(25)=2), and D is incorrect because we have the
population parameters.
5. For a sample size of 100, the standard error of the sample mean is 3.
If the sample size is increased to 400, what is the new standard error,
assuming population standard deviation remains constant?
A) 3
B) 6
C) 1.5
D) 0.75
Answer: C
, 4|Page
Explanation: Standard error = sigma/sqrt(n). If n quadruples from 100 to
400, sqrt(n) doubles, so the standard error is halved. = 1.5. Option
A is unchanged, B is doubled, D is quartered.
6. The law of large numbers states that:
A) As the sample size grows, the sample mean converges to the
population mean.
B) As the sample size grows, the sampling distribution becomes
perfectly normal.
C) Larger samples always eliminate bias.
D) The population variance decreases as sample size increases.
Answer: A
Explanation: The law of large numbers indicates that the sample
average approaches the expected value (population mean) as n
increases. Option B is the CLT, C is false because bias is a design issue, D
is false because population variance is fixed.
7. Which of the following is a parameter?
A) Sample proportion p-hat
B) Sample mean x-bar
C) Population standard deviation sigma
D) Sample standard deviation s
Answer: C
