Question 1

Which of the following is true about the sampling distribution of the sample mean?
A) The mean of the sampling distribution is always 
B) The standard deviation of the sampling distribution is always 
C) The shape of the sampling distribution is always approximately normal.
D) All of the above are true.

Accepted Answer

A

Question 2

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 exceeded $4.0 million.
A) Approximately 0
B) 0.0228
C) 0.9772
D) Approximately 1

Accepted Answer

The standard error of the mean is $1.2 million / sqrt(100) = $0.12 million. The z-score for $4.0 million is ($4.0 million - $3.26 million) / $0.12 million = 6.17. A z-score of 6.17 is extremely high, making the probability of the mean salary exceeding $4.0 million approximately 0.

Question 3

If the expected value of a sample statistic is equal to the parameter it is estimating, then we call
That sample statistic
A) unbiased.
B) minimum variance.
C) biased.
D) random.

Accepted Answer

An unbiased estimator is one where the expected value of the sample statistic equals the parameter it is estimating.

Question 4

True or False: The amount of time it takes to complete an examination has a left skewed
distribution with a mean of 65 minutes and a standard deviation of 8 minutes.If 64 students were
randomly sampled, the probability that the sample mean of the sampled students exceeds 71
minutes is approximately 0.

Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal for large sample sizes. Given the mean of 65 and standard deviation of 8, the probability of the sample mean exceeding 71 minutes is extremely low, approaching 0.

Question 5

Sales prices of baseball cards from the 1960s are known to possess a right skewed distribution
With a mean sale price of $5.25 and a standard deviation of $2.80.Suppose a random sample of
100 cards from the 1960s is selected.Describe the sampling distribution for the sample mean sale
Price of the selected cards.
A) Right skewed with a mean of $5.25 and a standard error of $2.80
B) Normal with a mean of $5.25 and a standard error of $0.28
C) Right skewed with a mean of $5.25 and a standard error of $0.28
D) Normal with a mean of $5.25 and a standard error of $2.80

Accepted Answer

The sampling distribution of the sample mean will be approximately normal due to the Central Limit Theorem, even though the population distribution is right-skewed. The mean of the sampling distribution will be the same as the mean of the population, which is $5.25. The standard error of the sampling distribution will be the standard deviation of the population divided by the square root of the sample size, which is $2.80 / sqrt(100) = $0.28.

Question 6

The Central Limit Theorem is important in statistics because
A) for a large n, it says the population is approximately normal.
B) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.
C) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.
D) for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

Accepted Answer

The Central Limit Theorem states that for a large n, the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. This makes choice C the correct answer. Choices A and B are incorrect because they only apply to populations that are already normal or have a large n. Choice D is also incorrect because it implies that the sampling distribution of the sample mean is always normal, which is not true for small sample sizes.

Question 7

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

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is large enough, regardless of the population's distribution, as long as the population mean and standard deviation are known.

Question 8

A sample that does not provide a good representation of the population from which it was
collected is referred to as a(n)sample.

Accepted Answer

The answer of A sample that does not provide a...

Question 9

Which of the following statements about the sampling distribution of the sample mean is
Incorrect?
A) The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large

B) The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means.
C) The mean of the sampling distribution of the sample mean is equal to μ.
D) The standard deviation of the sampling distribution of the sample mean is equal to σ.

Accepted Answer

The answer of Which of the following statements about the...

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.Find the
Approximate probability that the mean salary of the 100 players was no more than $3.0 million.
A) Approximately 0
B) 0.0151
C) 0.9849
D) Approximately 1

Accepted Answer

The standard error of the mean is $1.2 million / sqrt(100) = $0.12 million. The z-score for $3.0 million is ($3.0 million - $3.26 million) / $0.12 million = -2.17. The probability of a z-score being less than -2.17 is approximately 0.0151.

Question 11

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

Accepted Answer

The standard error (SE) is calculated as the standard deviation divided by the square root of the sample size: SE = $1.2 million / √100 = $0.12 million.

Question 12

The standard error of the mean
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.

Accepted Answer

The standard error of the mean is always less than or equal to the population standard deviation, decreases with larger sample sizes, and indicates the variability of sample means.

Question 13

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Accepted Answer

The answer of  ....

Question 14

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

Accepted Answer

The Central Limit Theorem allows us to disregard the shape of the population when n is large, and this is important in the study of sampling distributions as it means that we can make inferences about the population based on a more manageable sample size without requiring the population to be normally distributed.

Question 15

The distribution of the number of loaves of bread sold per week by a large bakery over the past 5
years has a mean of 7,750 and a standard deviation of 145 loaves.Suppose a random sample of n
= 40 weeks has been selected.What is the approximate probability that the mean number of
loaves sold in the sampled weeks exceeds 7,895 loaves?

Accepted Answer

The answer of The distribution of the number of loaves...

Question 16

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 exceeded $3.5 million.
A) Approximately 0
B) 0.0228
C) 0.9772
D) Approximately 1

Accepted Answer

The sampling distribution of the sample mean will be approximately normal with mean $3.26 million and standard deviation $1.2 million/sqrt(100) = $0.12 million. The z-score for $3.5 million is (3.5 - 3.26) / 0.12 = 2. The probability that the mean exceeds $3.5 million is the probability that a standard normal variable exceeds 2, which is approximately 0.0228.

Question 17

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 less than $2.5 million.
A) Approximately 0
B) 0.0151
C) 0.9849
D) Approximately 1

Accepted Answer

The answer of Major league baseball salaries averaged $3.26 million...

Question 18

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?
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.

Accepted Answer

The standard deviation of the sampling distribution (standard error) is not equal to 3 years; it is equal to the population standard deviation divided by the square root of the sample size, which is 0.3 years.

Question 19

Sampling distributions describe the distribution of
A) parameters.
B) statistics.
C) both parameters and statistics.
D) neither parameters nor statistics.

Accepted Answer

Sampling distributions describe the distribution of statistics, which are numerical summaries of samples taken from a population. Parameters are numerical summaries of the entire population and are not directly affected by sampling variability.

Question 20

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.
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.

Accepted Answer

According to the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (n=100 is large). The mean of the sampling distribution is the same as the population mean (10 minutes), and the standard error is the population standard deviation divided by the square root of the sample size (8/√100 = 0.8 minutes).

Quiz 7: Sampling Distributions

Which of the following is true about the sampling distribution of the sample mean?

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 exceeded $4.0 million.

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

The Central Limit Theorem is important in statistics because

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.

A sample that does not provide a good representation of the population from which it was collected is referred to as a(n)sample.

Which of the following statements about the sampling distribution of the sample mean is Incorrect?

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.

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?

The standard error of the mean

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

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 exceeded $3.5 million.

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 less than $2.5 million.

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?

Sampling distributions describe the distribution of