Question 1

Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of
23 years and a standard deviation of 3 years.If we randomly sampled 100 students, which of the
Following statements about the sampling distribution of the sample mean age is incorrect?

Accepted Answer

A)  The mean of the sampling distribution is equal to 23 years. 
B)  The standard deviation of the sampling distribution is equal to 3 years. 
C)  The shape of the sampling distribution is approximately normal. 
D)  The standard error of the sampling distribution is equal to 0.3 years.

Question 2

True or False: The sample proportion is an unbiased estimator for the population proportion.

Accepted Answer

A) True 
 B)False

Question 3

True or False: As the size of the sample is increased, the standard deviation of the sampling
distribution of the sample mean for a normally distributed population will stay the same.

Accepted Answer

A) True 
 B)False

Question 4

True or False: The sample mean is an unbiased estimate of the population mean.

Accepted Answer

A) True 
 B)False

Question 5

True or False: If the population distribution is skewed, in most cases the sampling distribution
of the mean can be approximated by the normal distribution if the samples contain at least 30
observations.

Accepted Answer

A) True 
 B)False

Question 6

The standard error of the mean for a sample of 100 is 30.In order to cut the standard error of the
Mean to 15, we would

Accepted Answer

A)  increase the sample size to 200. 
B)  increase the sample size to 400. 
C)  decrease the sample size to 50. 
D)  decrease the sample to 25.

Question 7

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in
A certain year in the past.Suppose a sample of 100 major league players was taken.Find the
Approximate probability that the mean salary of the 100 players was no more than $3.0 million.

Accepted Answer

A)  Approximately 0 
B)  0.0151 
C)  0.9849 
D)  Approximately 1

Question 8

The owner of a fish market has an assistant who has determined that the weights of catfish are
Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of
16 fish is taken, what would the standard error of the mean weight equal?

Accepted Answer

A)  0.003 
B)  0.050 
C)  0.200 
D)  0.800

Question 9

True or False: The Central Limit Theorem is considered powerful in statistics because it works
for any population distribution provided the sample size is sufficiently large and the population
mean and standard deviation are known.

Accepted Answer

A) True 
 B)False

Question 10

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in
A certain year in the past.Suppose a sample of 100 major league players was taken.What was the
Standard error for the sample mean salary?

Accepted Answer

A)  $0.012 million 
B)  $0.12 million 
C)  $12 million 
D)  $1,200.0 million

Question 11

True or False: Suppose μ = 50 and σ = 10 for a population.In a sample where n = 100 is
randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.

Accepted Answer

A) True 
 B)False

Question 12

True or False: In inferential statistics, the standard error of the sample mean assesses the
uncertainty or error of estimation.

Accepted Answer

A) True 
 B)False

Question 13

If the expected value of a sample statistic is equal to the parameter it is estimating, then we call
That sample statistic

Accepted Answer

A)  unbiased. 
B)  minimum variance. 
C)  biased. 
D)  random.

Question 14

For air travelers, one of the biggest complaints is of the waiting time between when the airplane
Taxis away from the terminal until the flight takes off.This waiting time is known to have a right
Skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes.Suppose
100 flights have been randomly sampled.Describe the sampling distribution of the mean waiting
Time between when the airplane taxis away from the terminal until the flight takes off for these
100 flights.

Accepted Answer

A)  Distribution is right skewed with mean = 10 minutes and standard error = 0.8 minutes. 
B)  Distribution is right skewed with mean = 10 minutes and standard error = 8 minutes. 
C)  Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes. 
D)  Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes.

Question 15

The owner of a fish market has an assistant who has determined that the weights of catfish are
Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.What
Percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

Accepted Answer

A)  84% 
B)  67% 
C)  29% 
D)  16%

Question 16

Why is the Central Limit Theorem so important to the study of sampling distributions?

Accepted Answer

A)  It allows us to disregard the size of the sample selected when the population is not normal. 
B)  It allows us to disregard the shape of the sampling distribution when the size of the population is large. 
C)  It allows us to disregard the size of the population we are sampling from. 
D)  It allows us to disregard the shape of the population when n is large.

Question 17

True or False: A sampling distribution is a distribution for a statistic.

Accepted Answer

A) True 
 B)False

Question 18

The standard error of the mean

Accepted Answer

A)  is never larger than the standard deviation of the population. 
B)  decreases as the sample size increases. 
C)  measures the variability of the mean from sample to sample. 
D)  All of the above.

Question 19

Sampling distributions describe the distribution of

Accepted Answer

A)  parameters. 
B)  statistics. 
C)  both parameters and statistics. 
D)  neither parameters nor statistics.

Question 20

True or False: If the amount of gasoline purchased per car at a large service station has a
population mean of 15 gallons and a population standard deviation of 4 gallons and a random
sample of 4 cars is selected, there is approximately a 68.26% chance that the sample mean will be
between 13 and 17 gallons.

Accepted Answer

A) True 
 B)False

Exam 7: Sampling Distributions

Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of 23 years and a standard deviation of 3 years.If we randomly sampled 100 students, which of the Following statements about the sampling distribution of the sample mean age is incorrect?

True or False: The sample proportion is an unbiased estimator for the population proportion.

True or False: As the size of the sample is increased, the standard deviation of the sampling distribution of the sample mean for a normally distributed population will stay the same.

True or False: The sample mean is an unbiased estimate of the population mean.

True or False: If the population distribution is skewed, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

The standard error of the mean for a sample of 100 is 30.In order to cut the standard error of the Mean to 15, we would

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in A certain year in the past.Suppose a sample of 100 major league players was taken.Find the Approximate probability that the mean salary of the 100 players was no more than $3.0 million.

The owner of a fish market has an assistant who has determined that the weights of catfish are Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of 16 fish is taken, what would the standard error of the mean weight equal?

True or False: The Central Limit Theorem is considered powerful in statistics because it works for any population distribution provided the sample size is sufficiently large and the population mean and standard deviation are known.

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in A certain year in the past.Suppose a sample of 100 major league players was taken.What was the Standard error for the sample mean salary?

True or False: Suppose μ = 50 and σ = 10 for a population.In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.

True or False: In inferential statistics, the standard error of the sample mean assesses the uncertainty or error of estimation.

If the expected value of a sample statistic is equal to the parameter it is estimating, then we call That sample statistic

The owner of a fish market has an assistant who has determined that the weights of catfish are Normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.What Percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

Why is the Central Limit Theorem so important to the study of sampling distributions?

True or False: A sampling distribution is a distribution for a statistic.

The standard error of the mean

Sampling distributions describe the distribution of