Question 1

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

A sample statistic is considered unbiased if its expected value is equal to the parameter it is estimating. This means that on average, the sample statistic is an accurate estimate of the true population parameter. Biased sample statistics, on the other hand, are systematically under- or over-estimating the true parameter, skewing the overall results.

Question 2

The professor of a business statistics class wanted to find out the mean amount of time per week her students spent studying for the class.She divided the students into the left,right and center groups according to the location they sat in the class that day.One of these 3 groups was randomly selected and everyone in the group was asked the mean amount of time per week he/she spent studying for the class.This is an example of a cluster sample.

Accepted Answer

The professor is dividing the students into groups based on their physical location in the class, which is an example of a cluster sample.

Question 3

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

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normal if the sample size is large enough, regardless of the shape of the population distribution. Here, with a sample size of 100, the distribution of the sample mean is approximately normal. The mean of the sampling distribution is the same as the population mean (10 minutes), and the standard error is calculated as the population standard deviation divided by the square root of the sample size, which is $8 / \sqrt{100} = 0.8$ minutes.

Question 4

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, not parameters. Parameters describe characteristics of a population, while statistics describe characteristics of a sample. Sampling distributions show the possible values the statistic could take under repeated sampling from the same population.

Question 5

The question: "How much did you earn last year rounded to the nearest hundreds of dollars?" will most likely result in measurement error.

Accepted Answer

This question may lead to rounding errors and may not accurately capture the exact amount earned. It may also be subject to response bias, as individuals may not feel comfortable disclosing their exact income.

Question 6

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 (CLT) states that the sampling distribution of the sample mean will approach a normal distribution as the sample size becomes large, regardless of the shape of the population distribution, provided the population has a finite mean and standard deviation. This makes it a powerful tool in statistics for making inferences about population parameters.

Question 7

Suppose a sample of n = 50 items is selected from a population of manufactured products and the weight,X,of each item is recorded.Prior experience has shown that the weight has a probability distribution with μ = 6 ounces and σ = 2.5 ounces.Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected?
A)The mean of the sampling distribution is 6 ounces.
B)The standard deviation of the sampling distribution is 2.5 ounces.
C)The shape of the sampling distribution is approximately normal.
D)All of the above are correct.

Accepted Answer

The answer of Suppose a sample of n = 50...

Question 8

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 states that when the sample size n is large (usually n > 30), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution. This is important because it allows us to make inferences about the population mean using the sample mean, even if the population distribution is not normal.

Question 9

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 answer of The amount of time it takes to...

Question 10

The question: "Have you used any form of illicit drugs over the past 2 months?" will most likely result in measurement error if the question is answered.

Accepted Answer

The question may result in measurement error as it relies on the honesty and accuracy of the respondent in admitting to illicit drug use. Some respondents may choose to underreport or deny drug use due to social desirability bias or fear of legal consequences.

Question 11

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

Accepted Answer

The mean of the sampling distribution is always equal to the population mean, μ. However, the standard deviation of the sampling distribution, known as the standard error, is equal to the standard deviation of the population divided by the square root of the sample size. While the shape of the sampling distribution may be approximately normal under certain conditions, it is not always the case. Therefore, only A is true.

Question 12

The average score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0.Suppose 36 pro golfers played the course today.Find the probability that the average score of the 36 pro golfers exceeded 71.

Accepted Answer

The answer of The average score of all pro golfers...

Question 13

Sampling error becomes an ethical issue if the findings are purposely presented without reference to sample size and margin of error so that the sponsor can promote a viewpoint that might otherwise be truly insignificant.

Accepted Answer

When the sample size and margin of error are intentionally left out, it becomes an ethical issue as it may deceive the audience and promote a false or insignificant viewpoint.

Question 14

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 answer of Suppose the ages of students in Statistics...

Question 15

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 sample size, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population. Therefore, option C is the best choice. Options A and D are incorrect because the Central Limit Theorem does not make any claims about the shape of the population itself or the size of the sample. Option B is partly correct, but it only applies to populations that are already normal or approximately normal.

Question 16

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 17

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 answer of The standard error of the mean
A)is never...

Question 18

The professor of a business statistics class wanted to find out the mean amount of time per week her students spent studying for the class.She divided the fifty students on her roster into ten groups starting from the first student on the roster.The first student was randomly selected from the first group.Then every tenth student was selected from the remaining students.This is an example of a cluster sample.

Accepted Answer

This is an example of a systematic sample because every tenth student was selected after the first student was chosen randomly, not a cluster sample where entire groups or clusters are chosen at random.

Question 19

Selection bias occurs more frequently in systematic samples than in simple random samples.

Accepted Answer

Systematic samples involve selecting every nth individual from the population, which may lead to excluding certain subgroups or patterns in the population, resulting in selection bias. Simple random samples, on the other hand, have an equal chance of selecting any individual from the population, reducing the potential for selection bias.

Question 20

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 (n ≥ 30).
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 standard deviation of the sampling distribution of the sample mean is not equal to σ, but rather equal to σ/√n, where σ is the population standard deviation and n is the sample size.

Quiz 7: Sampling and Sampling Distributions

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

Sampling distributions describe the distribution of

The question: "How much did you earn last year rounded to the nearest hundreds of dollars?" will most likely result in measurement error.

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.

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

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.

The question: "Have you used any form of illicit drugs over the past 2 months?" will most likely result in measurement error if the question is answered.

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

The average score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0.Suppose 36 pro golfers played the course today.Find the probability that the average score of the 36 pro golfers exceeded 71.

Sampling error becomes an ethical issue if the findings are purposely presented without reference to sample size and margin of error so that the sponsor can promote a viewpoint that might otherwise be truly insignificant.

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?

The Central Limit Theorem is important in statistics because

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

The standard error of the mean

Selection bias occurs more frequently in systematic samples than in simple random samples.

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