Question 1

In a sampling distribution of the mean, approximately percent of the sample means will be contained within the interval of two standard errors above and below the population mean.

Accepted Answer

According to the central limit theorem, approximately 95% of the sample means will fall within two standard errors above and below the population mean in a sampling distribution of the mean. This is also known as the 95% confidence interval.

Question 2

A population has a mean of 50 and a standard deviation of 8. If samples of size N = 16 are randomly drawn from this population, then the standard error will be equal to.

Accepted Answer

The formula for calculating standard error is standard deviation divided by the square root of the sample size: SE = σ/√n. 
Plugging in the values, we get SE = 8/√16 = 8/4 = 2.0. Thus, the standard error will be 2.0 in this case. So, the correct choice is B.

Question 3

Which of the following considerations influences how well a statistic estimates a parameter?

Accepted Answer

All of the options (sampling method, sample size, and variability in the population) can influence how well a statistic estimates a parameter. The sampling method affects whether the sample is representative of the population, the sample size affects the precision of the estimate, and the variability in the population affects the amount of error in the estimate. Therefore, all three factors impact how accurately the statistic can estimate the population parameter.

Question 4

The value of is used to estimate σ.

Accepted Answer

The sample standard deviation, s, is used to estimate the population standard deviation, σ, when we have a sample.

Question 5

The sampling distribution of the mean is.

Accepted Answer

The sampling distribution of the mean is a theoretical distribution that shows the range of possible means that could be obtained from repeated sampling from the same population. It is based on probability theory and provides important information about the variability of sample means.

Question 6

A sampling distribution of the mean can be described in terms of its.

Accepted Answer

A sampling distribution of the mean can be fully described in terms of its shape, mean, and standard deviation. The shape is determined by the underlying population and sample size. The mean of the sampling distribution of the mean is equal to the population mean, while the standard deviation is equal to the population standard deviation divided by the square root of the sample size. Therefore, all three options are necessary to fully describe a sampling distribution of the mean.

Question 7

If the sample mean has the same value as the population mean, then for that sample mean the.

Accepted Answer

Sampling error is the difference between the sample mean and population mean. If they have the same value, then the difference between the two is zero, so the sampling error is zero.

Question 8

A population has a mean of 100 and a standard deviation of 5. If samples of size N = 25 are randomly drawn from this population, then the standard error will be equal to.

Accepted Answer

The answer of A population has a mean of 100...

Question 9

The distribution of X values when all possible samples of size N are selected from a population is called a  distribution of the mean.

Accepted Answer

The distribution of X values when all possible samples of size N are selected from a population is called the sampling distribution of the mean.

Question 10

A theoretical probability distribution of values of a statistic resulting from selecting all possible samples of size N from a population is called a distribution of that statistic.

Accepted Answer

The description given fits the definition of a sampling distribution.

Question 11

As sample size increases, a sampling distribution of the mean will approximate a normal distribution, regardless of the shape of the distribution of scores in the population. This characteristic of the sampling distribution of the mean is stated in the.

Accepted Answer

The characteristic described is known as the central limit theorem, which states that as sample size increases, the sampling distribution of the mean will become approximately normally distributed, regardless of the shape of the population distribution.

Question 12

A frequency distribution of sample means obtained by actually selecting samples from a population and then computing the means of those samples is called a(n) sampling distribution of the mean.

Accepted Answer

A sampling distribution of the mean is based on actually selecting samples from a population, which is empirical data, rather than hypothetical or theoretical data. Therefore, option B, empirical, is the best choice.

Question 13

Which of the following statements is correct?

Accepted Answer

The larger the sample size, the closer the sample mean is to the population mean. This results in smaller sampling error.

Question 14

For population distributions that are not heavily skewed, many statisticians consider a minimum sample size of to produce a sampling distribution of the mean that will approximate a normal distribution.

Accepted Answer

The central limit theorem states that for sample sizes greater than or equal to 30, the sampling distribution of the mean will be approximately normal, regardless of the shape of the population distribution. Thus, a minimum sample size of 30 is recommended to produce an accurate approximation of the sampling distribution of the mean. Choices A and B are too small, and choice D is unnecessarily large.

Question 15

The standard error is the.

Accepted Answer

Standard error is the standard deviation of the sampling distribution of the mean. It represents how much the sample means deviate from the true population mean.

Question 16

Sampling error

Accepted Answer

Sampling error refers to the difference between the sample mean ($\bar { X }$) and the population mean ($\mu$). This error arises because the sample is only a part of the whole population, and there's a chance that the sample might not perfectly represent the population's characteristics.

Question 17

The central limit theorem indicates that as sample size increases, the theoretical sampling distribution of the mean.

Accepted Answer

The central limit theorem states that as the sample size increases, the sampling distribution of the mean will approach a normal distribution, regardless of the shape of the population distribution. Therefore, D is the best choice, as the distribution becomes more normal.

Question 18

A standard error of the mean is a standard deviation of a.

Accepted Answer

A standard error of the mean is the standard deviation of the sampling distribution of the mean, and reflects the variability in means that would be obtained from different samples taken from the same population.

Question 19

The error in estimating a population mean from a sample mean is called error.

Accepted Answer

The error in estimating a population mean from a sample mean arises due to the fact that the sample mean is only an estimate of the true population mean. This type of error is called sampling error. It occurs because the sample is only a subset of the population and may not perfectly represent it. Therefore, this error can be reduced by increasing the sample size, improving the sampling technique, and minimizing bias in the sample selection process. The other choices are not correct as they do not accurately describe the type of error that occurs in this situation.

Question 20

The theoretical sampling distribution of the mean.

Accepted Answer

The answer of The theoretical sampling distribution of the mean.
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Quiz 7: Understanding Data: Using Statistics for Inference and Estimation