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

Question 1

What are the three distributions involved in every application of inferential statistics?

A)sample,sampling,and population
B)sample,stratification,cluster
C)EPSEM,random,probability
D)sampling,percentage,normal

Answer 1

A

Question 2

There are about 70 million eligible voters in a society.A public opinion pollster has estimated their probable choices for the next president with a sample of 2,000 randomly selected citizens.In this example,the 2,000 citizens are a ____ and the 70 million eligible voters are a ____.

A)sampling distribution;sample distribution
B)population;cluster
C)cluster;proportion
D)sample;population

Answer 2

D

Question 3

Statistics are to parameters as

A)samples are to populations.
B)populations are to samples.
C)medians are to standard deviations.
D)percentages are to proportions.

Answer 3

A

Question 4

For a simple random sample,each case and each combination of cases in the population must

A)be representative.
B)be included in the sample.
C)be contacted by the researcher.
D)have an equal probability of being chosen for the sample.

Question 5

Samples are to populations as

A)big is to little.
B)central tendency is to dispersion.
C)measures are to variables.
D)statistics are to parameters.

Question 6

Compared to probability samples,non-probability samples

A)are usually cheaper to assemble.
B)are always much larger.
C)are usually more expensive to assemble.
D)allow for generalizations to populations.

Question 7

Both the sample and the population distributions are empirical,which means that they are

A)theoretical
B)real
C)ordinal
D)stratified

Question 8

A researcher questioned 45 randomly-selected members of the freshman class about their experiences drinking alcohol and used these responses to estimate the drinking behavior of the entire freshman class of 1500.In this example,the 45 interviewees were the ____ and the ____ was the population.

A)sample;student body
B)parameters;freshman class
C)statistics;parameters
D)sample;freshman class

Question 9

The goal of all techniques for selecting probability samples is to select samples that are

A)very large.
B)non-random.
C)easily located.
D)representative.

Question 10

If a sample is representative,it

A)is stratified.
B)is restricted to the calculation of parameters only.
C)reproduces the characteristics of the population.
D)resembles the sampling distribution

Question 11

The fundamental principle of probability sampling is that a sample selected by ____ is very likely to be ____.

A)EPSEM;representative
B)stratification;large
C)telephone polls;cheap
D)clusters;stratified

Question 12

The sampling distribution links the ____ to the ____.

A)stratified;EPSEM
B)statistical;empirical
C)sample;population
D)empirical;real

Question 13

A sample selected according to the principle of EPSEM is extremely likely to be

A)large.
B)biased.
C)representative.
D)inaccurate.

Question 14

Unless a sample is ____,it cannot be used to make accurate generalizations to a population.

A)very large
B)non-probability
C)representative
D)stratified

Question 15

Statistics are characteristics of samples while ____ are characteristics of ____.

A)percentages;populations
B)medians;clusters
C)parameters;stratified samples
D)parameters;populations

Question 16

Unlike the sample and population distributions,the sampling distribution is

A)empirical.
B)theoretical.
C)random.
D)EPSEM.

Question 17

To select a simple random sample,a researcher needs

A)a list of the population and system for selecting cases according to EPSEM.
B)a list of the sample and a well developed sampling distribution.
C)a sampling distribution and a table of random numbers.
D)a parameter and a cluster.

Question 18

A researcher tests a theory about sexism by administering a survey to the 200 students in her sociology classes.This sample is best characterized as a

A)cluster sample.
B)stratified random sample.
C)non-probability sample.
D)sampling distribution.

Question 19

I use the principle of EPSEM to select a sample from my church for an opinion poll.The sample

A)is guaranteed to be representative of the population.
B)has a high probability of being representative.
C)should never be larger than 100.
D)should be larger than the population.

Question 20

Social scientists gather data from samples instead of populations because

A)samples are much larger and more complete.
B)samples are more trustworthy.
C)populations are often too large to test.
D)samples are more meaningful and interesting.

Question 21

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.

Question 22

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.

Question 23

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.

Question 24

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.

Question 25

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.

Question 26

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.

Question 27

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

Question 28

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.

Question 29

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.

Question 30

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.

Question 31

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.

Question 32

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.

Question 33

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

A)statistics;parameters
B)parameters;statistics
C)values;frequencies
D)sample;populations

Question 34

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.

Question 35

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.

Question 36

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

A)sample.
B)sampling distribution.
C)population.
D)all of these

Question 37

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.

Question 38

The goal of estimation procedures is to infer ____ from ____.

A)intervals;estimates
B)bias;efficiency
C)statistics;parameters
D)parameters;statistics

Question 39

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) $\sigma / \sqrt { N }$

Question 40

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

Question 41

We can estimate the probability that sample means and proportions lie within a given distance of the population value because these statistics are

A)unbiased.
B)efficient.
C)random.
D)biaseD.

Question 42

In estimation procedures,the alpha level is

A)the same as the confidence level.
B)the parameter we are trying to estimate.
C)always greater than the standard error.
D)equal to the efficiency ratio minus the bias coefficient.

Question 43

An estimator is unbiased if the mean of its sampling distribution is equal to

A)the midpoint of the distribution.
B)the sample mean.
C)the population value.
D)the population median.

Question 44

Based on an EPSEM sample of 300 state university students,we estimate that the average number of hours of study time each week is 30 $\pm$ 2.In this example,the parameter is

A)300.
B)30.
C) $\pm$ 2.
D)unknown.

Question 45

A confidence level of 99% is the same as an alpha level of

A)0.05.
B)0.10.
C)0.01.
D)0.001.

Question 46

The sizes of four samples vary as follows:
Sample A,N = 100
Sample B,N = 76
Sample C,N = 1000
Sample D,N = 150
Which sample will produce the most efficient estimate?

A)Sample A
B)Sample B
C)Sample C
D)Sample D

Question 47

To increase the probability that a confidence interval will include the population parameter,

A)lower the alpha level.
B)raise the alpha level.
C)increase the bias of the sample statistiC.
D)set efficiency to zero.

Question 48

The larger the sample size (N),the

A)smaller the parameter.
B)greater the efficiency.
C)lower the bias.
D)larger the standard error of the mean.

Question 49

The efficiency of a sample estimator is essentially a matter of

A)accuracy
B)validity
C)centrality
D)dispersion

Question 50

The most commonly used confidence level is

A)99.5%.
B)95%.
C)90.5%.
D)90%.

Question 51

Two sample statistics are unbiased estimators.They are

A)means and proportions.
B)means and standard deviations.
C)medians and modes.
D)proportions and percentages.

Question 52

The probability that an interval estimate does not include the population value is called

A)the margin.
B)alpha.
C)an error.
D)the odds.

Question 53

The more efficient the estimate,the more the sampling distribution

A)is evenly spread from the mean to $\pm$ 2 standard deviations.
B)becomes flatter.
C)clusters to the right of the mean.
D)is clustered around the mean.

Question 54

In ____ of the cases,the mean of a sample selected by EPSEM will be more than $\pm$ 3 Z's from the population mean.

A)less than 1%
B)more than 5%
C)more than 90%
D)more than 99%

Question 55

An alpha level of 0.05 is the same as a confidence level of

A)99.5%.
B)95%.
C)90.5%.
D)90%.

Question 56

The probability that a sample mean is within $\pm$ 1 Z of the population mean is about

A).34.
B).68.
C).95.
D).99.

Question 57

Based on an EPSEM sample of 300 state university students,we estimate that the average number of hours of study time each week is 30 $\pm$ 2.In this example,the population is

A)the 300 state university students.
B)all state university students.
C)unknown.
D)the same as the parameter.

Question 58

In the United States,between 70% and 80% of the people who do the family grocery shopping are women.This is

A)not a finding which can be generalized.
B)a representative parameter.
C)an interval estimate.
D)sexism at its most offensive.

Question 59

The efficiency of any estimator can be improved by

A)increasing the sample size.
B)decreasing the sample size.
C)making the sample representative.
D)changing the sample.

Question 60

Because there is always a chance that an EPSEM sample might not be representative,alpha cannot be

A)known.
B)1.00.
C)0.00.
D)less than .10.

Question 61

In estimation procedures,the Z score that corresponds to an alpha of .05 is

A) $\pm$ 1.96.
B) $\pm$ 2.58.
C) $\pm$ 3.78.
D) $\pm$ 9.78.

Question 62

The greater the confidence level,the ____ width of the confidence interval

A)narrower
B)more representative
C)more efficient
D)wider

Question 63

A random sample of 500 reports an average yearly income of $42,000 with a standard deviation of $1000.An estimate of the parameter at the 95% level is about $175 wide.In this research situation

A)the parameter is $42,000.
B)the sample is unrepresentative.
C)the alpha level is 0.05.
D)the sample mean is $175.

Question 64

A random sample of 500 reports an average yearly income of $42,000 with a standard deviation of $1000.An estimate of the parameter at the 95% level is about $175 wide.In this research situation

A)we can be 95% confident that the population mean is 42,000 $\pm$ 175.
B)the sample size is much too small to justify the use of estimation procedures.
C)the alpha level is 1000.
D)the sample mean is $175.

Question 65

Polls tracking the presidential election of 2004 showed that

A)Bush lead by a clear margin from start to finish.
B)Kerry lead by a clear margin until just a week before election day.
C)the race was "too close to call" during much of the campaign.
D)voter turnout would be extraordinarily high.

Question 66

In estimation procedures,as the alpha level decreases,the corresponding Z score

A)moves closer to the mean of the sampling distribution.
B)moves away from the mean of the sampling distribution.
C)becomes negative.
D)becomes positive.

Question 67

To construct the narrowest possible confidence intervals,use ____.

A)small samples
B)large samples
C)the least efficient estimator
D)an unbiased statistic

Question 68

We have used an alpha of 0.01 to estimate the average hours of television viewing for residents in a retirement home.What is the chance that our interval estimate does not contain the true population mean?

A)99%
B)10%
C)1%
D)1/10 of 1%

Question 69

Polls tracking the popularity of President Bush show

A)dramatic increases in support following both the terrorist attacks of 9/11 and the invasion of Iraq.
B)a dramatic increase in support following 9/11 but no particular change after the invasion of Iraq.
C)a remarkable consistency in popularity that never exceeded 55% and never fell below 50%.
D)low levels of support that have often fallen below 25% approval.

Question 70

A random sample of 200 includes 100 Protestants.The researcher estimates at the 95% confidence level that between 43% and 57% of the population is Protestant.In this research situation

A)the parameter is 200.
B)P_u is .43 or .57.
C)N is 100.
D)alpha is 0.05.

Question 71

The sample standard deviation is a biased estimator of the population standard deviation.When using sample means as estimators,we correct for bias in the formula for finding confidence intervals by

A)using N - 1 rather than N.
B)using N rather than N - 1.
C)using s rather than Z.
D)squaring the value of Z.

Question 72

Wider confidence intervals

A)are sure to include the population value.
B)are less likely to include the population value.
C)are more likely to include the population value.
D)do not alter the chance of including the population value.

Question 73

When using sample means as estimators,we usually estimate the population standard deviation with

A)the sample standard deviation.
B)the sampling distribution standard deviation.
C)the population parameter.
D)the Z score.

Question 74

All other things being equal,larger sample will cost more to process

A)but will not necessarily have narrower confidence intervals.
B)and will always produce narrower confidence intervals.
C)and will always produce wider confidence intervals.
D)but will produce more precise intervals if the confidence level is low.

Question 75

Which sample size will produce the confidence interval with the smallest width?

A)100
B)200
C)500
D)1000

Question 76

As our confidence in an interval estimate increases,the width of the interval

A)decreases.
B)increases.
C)remains the same.
D)increases or decreases depending on the alpha level.

Question 77

The width of an interval estimate can be controlled by

A)changing the confidence level.
B)changing the alpha level.
C)changing the sample size.
D)any of these

Question 78

A random sample of 200 includes 100 Protestants.The researcher estimates at the 95% confidence level that between 43% and 57% of the population is Protestant.In this research situation

A)alpha is .10.
B)P_u is 95.
C)N is 100.
D)P_s is .50.

Question 79

Sample size and the width of confidence intervals

A)increase at the same rate
B)increase at different rates: sample size increases faster than interval width
C)increase at different rates: sample size increases more slowly than interval width
D)have no relationship to each other.

Question 80

The average weight of a sample of women who attend aerobics classes at the YWCA is 130 pounds.We construct a confidence interval (using an alpha of 0.05)of $\pm$ 3.45.The upper and lower limits of our estimate are

A)130.00 and 133.45.
B)126.55 and 130.45.
C)126.55 and 133.45.
D)unknown;these values will depend on the number of women who are truly serious about exercising.