Question 1

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 2

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 3

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 4

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 of the sample mean is always equal to the population mean μ. However, the standard deviation of the sampling distribution of the sample mean is given by σ/√n, where σ is the population standard deviation and n is the sample size. The shape of the sampling distribution of the sample mean is not always approximately normal, but it becomes more normal as the sample size increases due to the Central Limit Theorem.

Question 5

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.

Question 6

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

Sampling error is a common issue in research, but it becomes an ethical issue if the findings are purposely presented without appropriate reference to sample size and margin of error. This can lead to a sponsor promoting a viewpoint that might be insignificant or misleading, which is unethical.

Question 7

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 the population standard deviation, σ. Instead, it is equal to σ/√n, where n is the sample size.

Question 8

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 enough sample size (n), the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population. This is important in statistics because it allows us to make inferences about a population parameter based on a sample mean.

Question 9

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 sampling method described is cluster sampling, which involves dividing the population into clusters or groups and randomly selecting one or more clusters to sample from. In this case, the clusters are based on the location of the students in the class.

Question 10

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 sample statistic is one for which the expected value is equal to the parameter it is estimating. This means that on average, over many samples, the sample statistic will come close to the true value of the population parameter. If the expected value of the sample statistic is not equal to the population parameter, we call it biased. A minimum variance statistic is one that has the smallest possible variance, but this does not necessarily mean it is unbiased. Randomness is a property of the sampling procedure used to obtain the sample, not of the sample statistic itself.

Question 11

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

This question is asking about sensitive information, and individuals may be hesitant to disclose or may feel shame or fear of consequences for admitting illicit drug use. As a result, there is a risk of underreporting or even lying, leading to measurement error.

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

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

Accepted Answer

Selection bias is more likely in systematic sampling because the method involves selecting elements from a list at regular intervals, which can inadvertently favor certain patterns within the population. In contrast, simple random sampling, where every member of the population has an equal chance of being selected, minimizes the risk of such bias.

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 states that as the sample size (n) increases, the sampling distribution of the sample mean becomes 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 and standard deviation, even when the population distribution is not known or not normal.

Question 15

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 is likely to result in measurement error because rounding to the nearest hundreds of dollars can lead to significant differences in earnings. For example, someone who earned $29,950 may round to $30,000 while someone who earned $30,049 may round to $30,100, resulting in a significant difference in reported earnings.

Question 16

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 17

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 18

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...

Question 19

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 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

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.

Quiz 7: Sampling and 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?

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

Sampling distributions describe the distribution of

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.

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

The Central Limit Theorem is important in statistics because

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