Question 1

The Central Limit Theorem states that as sample size becomes large
A)the sampling distribution of sample means approaches normality.
B)the sampling distribution of sample means becomes larger.
C)the population distribution becomes normal.
D)the sample distribution becomes normal.

Accepted Answer

The Central Limit Theorem states that as sample size becomes large, the sampling distribution of sample means approaches normality. This means that as the sample size increases, the distribution of sample means will become more and more normal, regardless of the shape of the population distribution.

Question 2

By the theorems presented in the text,we know that the mean of a sampling distribution of sample means will be
A)the same as the population mean.
B)close to the value of the sample mean.
C)between the population and sample means in value.
D)representative of the entire population.

Accepted Answer

Theorems state that the mean of a sampling distribution of sample means will be the same as the population mean.

Question 3

The standard error of the mean is the same thing as
A)the standard deviation of a sample.
B)the standard deviation of a population.
C)the standard deviation of a sampling distribution.
D)the variance of a sample.

Accepted Answer

The standard error of the mean (SEM) is the standard deviation of the sampling distribution of the sample means. It is a measure of how much variability there is in the means of different samples drawn from the same population. Therefore, the SEM is not the same thing as the standard deviation of a sample (choice A) or the standard deviation of a population (choice B). The variance of a sample (choice D) is related to the standard deviation, but they are not the same thing, and the SEM is specifically related to the distribution of sample means.

Question 4

Public opinion polls and election projections are examples of
A)estimation procedures.
B)hypothesis testing.
C)non-statistical research methods.
D)blatant misuse of statistical procedures.

Accepted Answer

Public opinion polls and election projections are both examples of estimation procedures because they attempt to estimate the attitudes or voting behavior of a large population based on a smaller sample of respondents. Hypothesis testing and non-statistical research methods do not apply in this scenario, and while statistical misuse can occur, it is not necessarily inherent in the use of public opinion polls and election projections.

Question 5

The mean age of all college graduates is 35.If the population distribution is normal,the mean of any sampling distribution of sample mean ages of college graduates will be
A)within plus or minus 1 standard deviation of 35.
B)close to 35.
C)35.
D)determined by the size of the distribution.

Accepted Answer

The sampling distribution of the mean will also have a mean of 35, regardless of the sample size or standard deviation. This is a property of the central limit theorem.

Question 6

The shape of the sampling distribution of sample means can be assumed to be normal when N is
A)a large percentage of the population.
B)any number as long as you know the value of the population mean.
C)100 or more.
D)at least twice the value of the population standard deviation.

Accepted Answer

The shape of the sampling distribution of sample means can be assumed to be normal when the sample size is 100 or more, which satisfies the Central Limit Theorem. Even if the population distribution is not normal, the sampling distribution of sample means will tend towards a normal distribution with a large enough sample size. The options A, B, and D are inaccurate statements.

Question 7

The purpose of inferential statistics is to acquire knowledge of the ____ from the ____ by means of the ____ distribution
A)population;sample;sampling
B)sample;sampling;population
C)inductive;empirical;stratified
D)theoretical;empirical;theoretical

Accepted Answer

Inferential statistics allows us to make inferences about the population based on the sample by using probability distributions, specifically the sampling distribution. Therefore, the correct choice is A, which states the purpose of inferential statistics is to acquire knowledge of the population from the sample by means of the sampling distribution.

Question 8

In a sampling distribution of sample means,most of the sample means will
A)cluster around the true population value.
B)be below the population mean in value.
C)be above the population mean in value.
D)not follow any particular pattern.

Accepted Answer

In a sampling distribution of sample means, the Central Limit Theorem states that as the sample size increases, the distribution of sample means will become normal, with a mean equal to the true population mean. Therefore, most of the sample means will cluster around the true population value.

Question 9

Your sample size is 1000.It is safe to assume that
A)the shape of the sampling distribution of sample means is normal.
B)the sample is representative of the population.
C)the population distribution is normal.
D)the sample distribution is normal.

Accepted Answer

The central limit theorem states that for a sample size of 30 or greater, the sampling distribution of sample means will be approximately normal regardless of the distribution of the population. Since the sample size in this scenario is 1000, it is safe to assume that the shape of the sampling distribution of sample means is normal.

Question 10

According to the theorems presented in Chapter 7,we can be sure that the sampling distribution is normal if
A)the population is small.
B)the population is normal.
C)the sample is stratified.
D)the sample is normal.

Accepted Answer

According to the Central Limit Theorem, if the population is normal, the sampling distribution will also be normal, regardless of the sample size.

Question 11

With a sample size of 75,a normal sampling distribution can be assumed if
A)the cases in the sample are homogeneous.
B)the cases in the sample are heterogeneous.
C)the population distribution is normal.
D)the sample distribution is normal.

Accepted Answer

The normality of the population distribution, not the homogeneity or heterogeneity of the sample or the normality of the sample distribution, determines whether a normal sampling distribution can be assumed. Therefore, the best choice is C, as it indicates that the population distribution is normal.

Question 12

When we use larger samples (N > 100),we can assume a normal sampling distribution because of
A)common sense.
B)the Central Limit Theorem.
C)what we know about the population.
D)what we know about the sample.

Accepted Answer

The Central Limit Theorem states that as sample size increases, the sampling distribution of the mean approaches a normal distribution regardless of the population distribution. Therefore, when we use larger samples (N > 100), we can assume a normal sampling distribution based on statistical theory rather than common sense, knowledge about the population or knowledge about the sample.

Question 13

In estimation procedures,____ are estimated based on the value of ____.
A)statistics;parameters
B)parameters;statistics
C)values;frequencies
D)sample;populations

Accepted Answer

In estimation procedures, parameters (unknown values of the population) are estimated based on the value of statistics (known values of the sample). Therefore, option B is the correct choice. Options A, C, and D are incorrect as they either mix up the definitions of statistics and parameters or refer to irrelevant concepts such as frequencies or populations.

Question 14

The theorems presented in Chapter 7 tell us that if a sample is "large" the sampling distribution will be
A)the same shape as the population.
B)normal.
C)small.
D)irrelevant.

Accepted Answer

The central limit theorem tells us that if the sample size is "large" (usually considered to be at least 30), the sampling distribution will be approximately normal, regardless of the shape of the population. Therefore, the best choice is B, which indicates that the sampling distribution will be normal.

Question 15

I surveyed 48 randomly-selected residents of the apartment complex where I live to determine their voting habits.I can only use this information to generalize to all the residents if
A)there is evidence of a normal population distribution.
B)the 48 residents all have the same voting habits.
C)the 48 residents are equally divided in their voting habits.
D)the sample distribution is not normal in shape.

Accepted Answer

In order to generalize to all residents, we need to assume that the population distribution is normal. This is because many statistical tests and methods rely on the assumption of normality. If the population distribution is not normal, our results may not be accurate or may not be generalizable to the entire population.

Question 16

The General Social Survey (GSS)is an example of a
A)sample.
B)sampling distribution.
C)population.
D)all of these

Accepted Answer

The General Social Survey is a survey conducted on a sample of individuals to gather information about attitudes, beliefs, and behaviors of the general population. Therefore, it is an example of a sample. Sampling distribution refers to the distribution of sample statistics, and population refers to the entire group of individuals being studied, which is not the case with the GSS.

Question 17

In comparing a sampling distribution with a population distribution,
A)there will always be more variance in the sampling distribution.
B)there will always be more variance in the population distribution.
C)as the size of the sample increases the two distributions will become identical.
D)the two distributions will always be the same.

Accepted Answer

The answer of In comparing a sampling distribution with a...

Question 18

The goal of estimation procedures is to infer ____ from ____.
A)intervals;estimates
B)bias;efficiency
C)statistics;parameters
D)parameters;statistics

Accepted Answer

Estimation procedures are used to infer parameters from statistics. Parameters are generally unknown characteristics of populations, while statistics are computed from samples. Estimation procedures help us make educated guesses about the population based on our sample data.

Question 19

The standard deviation of the sampling distribution is represented by which of the following symbol(s)?
A) $\sigma / \mathrm { N }$
B) $(\sigma) (\mathrm { N })$
C) $\sqrt { \sigma/ N }$
D) $\sigma / \sqrt { N }$

Accepted Answer

The standard deviation of the sampling distribution is represented by $\sigma / \sqrt { N }$, which is D. This formula takes into account the size of the sample (N) and the population standard deviation ($\sigma$), and represents the variability of the means of all possible samples of size N taken from the population.

Question 20

Using the General Social Survey as an example,the concept of the sampling distribution allows us to link the sample of about ____ respondents to the population of about ____ adult Americans
A)10,000;200 million
B)225 million;3000
C)1 million;300 million
D)3,000 or 4,000;225 million

Accepted Answer

The General Social Survey is typically conducted with a sample of 3,000 or 4,000 adult Americans. Therefore, the best choice is D, which connects this sample size to the population of approximately 225 million adults in the United States. Choices A, B, and C are not accurate in terms of the number of respondents in the sample or the size of the corresponding population.

Quiz 7: Introduction in Inferential Statistics, the Sampling Distribution, and Estimation

The Central Limit Theorem states that as sample size becomes large

By the theorems presented in the text,we know that the mean of a sampling distribution of sample means will be

The standard error of the mean is the same thing as

Public opinion polls and election projections are examples of

The mean age of all college graduates is 35.If the population distribution is normal,the mean of any sampling distribution of sample mean ages of college graduates will be

The shape of the sampling distribution of sample means can be assumed to be normal when N is

The purpose of inferential statistics is to acquire knowledge of the from the by means of the distribution

In a sampling distribution of sample means,most of the sample means will

Your sample size is 1000.It is safe to assume that

According to the theorems presented in Chapter 7,we can be sure that the sampling distribution is normal if

With a sample size of 75,a normal sampling distribution can be assumed if

When we use larger samples (N > 100) ,we can assume a normal sampling distribution because of

In estimation procedures, are estimated based on the value of .

The theorems presented in Chapter 7 tell us that if a sample is "large" the sampling distribution will be

I surveyed 48 randomly-selected residents of the apartment complex where I live to determine their voting habits.I can only use this information to generalize to all the residents if

The General Social Survey (GSS) is an example of a

In comparing a sampling distribution with a population distribution,

The goal of estimation procedures is to infer from .

The standard deviation of the sampling distribution is represented by which of the following symbol(s) ?

Using the General Social Survey as an example,the concept of the sampling distribution allows us to link the sample of about respondents to the population of about adult Americans