Deck 7: Estimation and Sampling Distributions

Question 1

In the absence of any other information,the ____ is your best guess about the population mean.

A)sample mean with N-1 in the denominator
B)sample mean
C)sample mean with a correction factor in the numerator

Answer 1

sample mean

Question 2

If you selected every possible random sample of size N from some population,then the average (i.e.,mean)of the sample means will be ____.

A)zero
B)equal to ì
C)less than ì
D)more than ì

Answer 2

equal to ì

Question 3

Which of the following is an unbiased estimator of it's corresponding population parameter?

A)
B)s²

Answer 3

Question 4

An unbiased estimator of a population parameter is one whose average (mean)over all possible random samples of a given size equals the value of the:

A)sample mean
B)standard deviation
C)parameter in question
D)statistic

Question 5

The fact that a sample statistic may not equal the value of its corresponding population parameter is said to be the result of:

A)sampling error
B)systematic error
C)random error
D)parametric error

Question 6

The term "sampling error" reflects the fact that sample values are likely to differ from population values because:

A)mistakes have been made in the collection and analysis of the data
B)they are based on only a portion of the overall population
C)bias has contaminated the variance estimates
D)all of these

Question 7

In statistical terms,the sample mean is said to be a(n)_____ of the population mean.

A)biased estimator
B)unbiased estimator
C)standard estimator
D)underestimate

Question 8

To correct for the discrepancy between the sample variance (s²)and the population variance (ó²)we divide SS by _____.

A)N - 1
B)N
C)N - 2
D)

Question 9

In the absence of any other information,the sample mean that one observes is _____ of the value of the population mean.

A)a biased estimator
B)an underestimation
C)a conservative estimate
D)one's "best guess"

Question 10

In practice,it is _____ to compute the exact amount of sampling error that occurs.

A)unnecessary
B)difficult
C)impossible
D)relatively easy

Question 11

An unbiased estimator of the population variance can be obtained from sample data by dividing the sum of squares by:

A)N
B)N - 1
C)N - 2
D)none of these

Question 12

Statisticians have determined that the sample variance is a(n)_____ estimator of the population variance in that it _____ the population variance across all possible random samples of a given size.

A)unbiased;accurately estimates
B)unbiased;overestimates
C)biased;overestimates
D)biased;underestimates

Question 13

A(n)____ of a population parameter is one whose average over all possible random samples of a given size equals the value of the parameter.

A)estimator
B)unbiased estimator
C)biased estimator

Question 14

Which of the following situations is most likely to produce a random sample?

A)a selection procedure that reduces the chances of selecting improbable events
B)balancing the sample with both improbable and probable elements of the population
C)a selection procedure devised so that each element in the population is equally likely to be selected
D)all of these

Question 15

Your best guess of the true population variance is the ___.

A)sample variance
B)SS/N
C)variance estimate
D)
²

Question 16

The sample variance,on average,____the true population variance.

A)always equals
B)overestimates
C)underestimates
D)none of these

Question 17

Estimating population parameters can be accomplished with reference to _____ populations.

A)small
B)large
C)infinite
D)all of these

Question 18

When attempting to estimate a population parameter from a small sample,____ occurs.

A)experimenter bias
B)distribution error
C)sampling error
D)no error

Question 19

Which of the following is an unbiased estimator of the population variance:

A)SS/N
B)SS/N - 1
C)(SS - 1)/N
D)Ó(
- ì)

Question 20

The amount of sampling error can be represented as the difference between the value of a _____ and the value of the corresponding _____.

A)standard deviation;variance
B)sample statistic;population parameter
C)sample;population
D)mean;standard deviation

Question 21

If you were provided a set of 8 scores,____ would correspond to the degrees of freedom associated with the sum of squares of the 8 scores.

A)7
B)8
C)6
D)none of these

Question 22

If the standard error of the mean is small,then all the sample means based on a given sample size (N)will tend to be _____ and all will tend to be _____ the population mean.

A)small;equal to
B)similar;close to
C)dissimilar;far away from
D)large;equal to

Question 23

Technically,the accuracy of a variance estimate is not a function of the _____,but rather is a function of the _____.

A)degrees of freedom;sample size
B)sample size;degrees of freedom
C)degrees of freedom;standard error
D)sample size;population size

Question 24

The sampling distribution of the mean can be generated by drawing random samples of ____ and forming a frequency distribution of all means.

A)different sizes
B)the same size
C)increasingly larger sizes
D)none of these

Question 25

The symbols for the sample variance and population variance are ____ and ____,respectively.

A)ó;ó²
B)s²;s²
C)ó;s²
D)s²;ó²

Question 26

One result of the central limit theorem is that the _____ of a sampling distribution of the mean is always equal to the _____.

A)mean;sample mean
B)standard error;population variance
C)standard error;population mean
D)mean;population mean

Question 27

A sum of squares around a sample mean will always have _____ degrees of freedom associated with it.

A)several
B)N
C)2
D)N - 1

Question 28

In statistics,the phrase _____ is used to indicate the number of pieces of information that are "free of each other" in the sense that they cannot be deduced from one another.

A)degrees of freedom
B)degrees of deduction
C)degrees of independence
D)degrees of information

Question 29

The statistical phrase "degrees of freedom" denotes ____.

A)the number of related pieces of information
B)the number of independent pieces of information

Question 30

Calculate the unbiased estimate of the population mean from the following sample data: 4,5,4,3,2.

A)3.5
B)18/N - 1
C)3.6
D)5.2

Question 31

Which of the following values is the best estimate of the population mean using the following sample data: 4,4,4,5,5?

A)4.40
B)4.4/N - 1
C)3.5
D)22/N - 1

Question 32

A theoretical distribution consisting of the mean scores of all possible random samples of a given size that could be drawn from a population is called the ____.

A)variance estimate
B)population
C)sampling distribution of the mean
D)the central limit theorem

Question 33

Perspectives on the mean and standard deviation of a sampling distribution of the mean,as well as its shape,are derived from an important formulation called the:

A)central tendency theorem
B)central distribution theorem
C)central limit theorem
D)central estimate theorem

Question 34

The standard deviation of a sampling distribution of the mean is called the:

A)standard deviation estimate
B)standard error of the mean
C)sum of squared errors
D)none of these

Question 35

In general,estimation of a population parameter becomes more accurate as ____.

A)df of the sample increases
B)df of the sample decreases
C)population size increases
D)none of these

Question 36

Calculate the unbiased estimate of the population variance using the following sample data: 2,3,4,5,5.

A)1.360
B)1.304
C)1.166
D)1.700

Question 37

As the degrees of freedom associated with an estimate _____,the accuracy of the estimate tends to _____.

A)increase;decrease
B)decrease;increase
C)increase;increase
D)decrease;stay the same

Question 38

Irrespective of its specific computation,any sum of squares divided by its associated degrees of freedom is referred to as a:

A)variance estimate
B)standard deviation estimate
C)mean square
D)a and c

Question 39

The standard error of the mean reflects the accuracy with which _____ estimate a _____.

A)sample means;population mean
B)sample variances;population variance
C)samples;population
D)standard deviations;standard error

Question 40

A _____ can be formally defined as a theoretical distribution consisting of the mean scores for all possible random samples of a given size that could be drawn from a population.

A)sampling distribution of the mean
B)sampling distribution of the sample
C)sampling distribution of the scores
D)none of these

Question 41

The mean square is computed as ____.

A)SS/df
B)variance estimate/N - 1
C)both a and b
D)MS/N - 1

Question 42

Two factors influence the size of the standard error of the mean: the _____ and the _____.

A)sample standard deviation;sample variance
B)population size;variability of scores in the population
C)sample size;variability of scores in the population
D)sum of squares;error variance

Question 43

The sampling distribution of the mean can be approximated with a normal distribution given a sufficiently large sample size,regardless of the shape of the:

A)underlying population
B)underlying sample
C)normal distribution
D)sampling distribution

Question 44

Sampling from a finite population _____ is analogous to sampling from an infinite population _____.

A)with replacement;with replacement
B)without replacement;with replacement
C)with replacement;without replacement
D)without replacement;without replacement

Question 45

The variability of a sampling distribution is measured by the ____.

A)standard error of the mean
B)population variance
C)standard deviation estimate
D)sample variance estimate

Question 46

Given: ì = 3.5,ó = 2.09.Calculate ó for sample size of 16.

A)7.656
B).131
C).5225
D).539

Question 47

The formula for calculating the standard deviation of a sampling distribution of the mean is ____.

A)SS/N - 1
B)ó²/N
C)ó/
D)ó²/

Question 48

As the variability of scores in the population decreases,the standard error of the mean _____,other things being equal.

A)remains constant
B)fluctuates
C)increases
D)decreases

Question 49

For the following scores,what is the estimated standard error of the mean: 3,4,5,6,6,6,7,8,9

A).62
B).21
C).59
D).20

Question 50

The standard error of the mean can be reduced by ___.

A)increasing sample size
B)reducing ó
C)both a and b

Question 51

If the population mean is known to be 15,what would you conclude if you calculated a sample mean from this population to be 13?

A)an error has been made in calculating the sample mean
B)an error has been made in calculating the standard error of the mean
C)the sample mean is not representative of the population mean

Question 52

If you were to select a sample size that included the entire set of population scores,then the standard deviation of the sampling distribution based on that N would always equal ____.

A)1.00
B)ó
C)0
D)ó²

Question 53

When the sample size is greater than around 40,the normal approximation of the sampling distribution of the mean is:

A)biased
B)quite good
C)positively skewed
D)variable

Question 54

The central limit theorem states that a sampling distribution of the mean for a population will approximate that of a normal distribution as ____.

A)the shape of the distribution becomes more bell-shaped
B)sample size increases
C)sample size decreases
D)skewness decreases

Question 55

The sample mean is a(n)_____ estimator of the population mean because it _____ the population mean across all possible random samples of a given size.

A)biased;underestimates
B)biased;overestimates
C)unbiased;equals
D)unbiased;underestimates

Question 56

An implication of the central limit theorem is that the sampling distribution of the mean can be approximated by a _____ distribution when the sample size is sufficiently _____.

A)normal;large
B)normal;small
C)binomial;small
D)binomial;large

Question 57

According to the central limit theorem,the mean of the sampling distribution ____ the mean of the population.

A)is somewhat less than
B)is slightly greater than
C)greatly underestimates
D)is always equal to

Question 58

To estimate the standard error of the mean we use___.

A)s
B)s²/
C)s/
D)none of these

Question 59

Given the same population,the sampling distribution of the mean will show _____ than either the sampling distribution of the median or the sampling distribution of the mode.

A)greater accuracy
B)greater variability
C)less accuracy
D)less variability

Question 60

As the sample size increases,the standard error of the mean _____,other things being equal.

A)remains constant
B)fluctuates
C)increases
D)decreases

Question 61

The difference between the sample variance and the variance estimate is that the variance estimate _____:

A)underestimates the population variance
B)is computed with N-1 in the denominator
C)is computed with the degrees of freedom in the denominator
D)both b and c

Question 62

According to the central limit theorem,the sampling distribution of the mean approximates a _____ distribution as the sample size _____.

A)normal;becomes smaller
B)skewed;becomes smaller
C)normal;approaches infinity
D)skewed;approaches infinity
E)none of these

Question 63

In statistics,the phrase _____ refers to the number of pieces of information that are "independent of each other" in that they cannot be deduced from one another.

A)degrees of freedom
B)degrees of deduction
C)degrees of independence
D)degrees of information

Question 64

Other things being equal,as the population standard deviation becomes larger,the
Standard error of the mean

A)becomes smaller
B)becomes larger
C)stays the same
D)sometimes becomes smaller,sometimes becomes larger

Question 65

The symbol s represents

A)the sample standard deviation.
B)the variance estimate.
C)the population standard deviation.
D)the standard deviation estimate.

Question 66

The "correction" of subtracting 1 from N in the denominator makes the variance estimate _____ than the sample variance,and hence the variance estimate will be _____ the true population variance than the sample variance,on average.

A)smaller;closer to
B)larger;closer to
C)smaller;farther from
D)larger;farther from

Question 67

The standard deviation of the sampling distribution of the mean is

A)the standard deviation of the mean.
B)the standard error of the mean.
C)the sampling distribution of the standard deviation.
D)the population standard deviation.

Question 68

You ask a random sample of 75 people to complete a measure of verbal ability,and you want to estimate the variance in the population.How many degrees of freedom do you have for this variance estimate?

A)73
B)74
C)75
D)unlimited

Question 69

The mean of the sampling distribution of the mean is always equal to

A)the population mean.
B)the population mean minus one.
C)the population mean minus the sampling error.
D)the population mean plus the sampling error.

Question 70

The sampling distribution of the mean contains

A)raw scores from all members of the population.
B)the standard deviations computed from all possible random samples from a population.
C)the means of all possible random samples of a given size from a population.
D)a distribution of the standard error of the mean.

Question 71

Which of the following formulas for the mean would be used if a researcher is only interested in describing a sample without making inferences to a population?

A)
B)
C)
D)

Question 72

Which of the following formulas for the variance would be used if a researcher is interested in inferring what the population value would be?

A)
B)
C)
D)

Question 73

200 students scored a mean of 500 with a sum of squares of 1000 on the SAT-Verbal test.What is variance estimate?

A)2.242
B)2.236
C)5.000
D)5.025

Question 74

If the population standard deviation is 15,and the sample size is 500,what is the standard error of the mean?

A)0.03
B)0.67
C)33.33

Question 75

The sample variance can be changed so that it becomes an unbiased estimator of the population by changing the calculation so that

A)N is in the denominator of the formulA.
B)the mean square is in the numerator of the formula.
C)a correction of N-1 is in the denominator of the formula.
D)a correction of SS-1 is in the numerator of the formula.

Question 76

The sample variance _____ the population variance across all possible samples of a given size.

A)underestimates
B)overestimates
C)equals
D)will either over- or underestimate (depending on the sample size.

Question 77

Other things being equal,as the sample size becomes larger,the standard error of the mean

A)becomes smaller.
B)becomes larger.
C)stays the same.
D)sometimes becomes smaller,sometimes becomes larger.

Question 78

If a researcher is interested in having a group of 100 people complete a survey and she plans to calculate a variance estimate and standard deviation estimate for that group,how can she increase her degrees of freedom before she does her calculations?

A)Do not use a correction in the denominator of the variance calculation.
B)Have more than 100 people complete the survey.
C)Reduce variability of the sample by collecting information from a homogeneous group.
D)Include a mean square calculation for the standard deviation estimate.

Question 79

In most behavior science research a goal is to describe very large groups of people.This would be considered a(n)_____.

A)infinite population
B)finite population
C)unbiased estimate of the population
D)biased estimate of the population

Question 80

The variance estimate is an example of a

A)degree of freedom.
B)mean square.
C)sampling distribution of the variance.
D)population parameter.