Deck 17: Determination of Sample Size: A Review of Statistical Theory

Question 1

"As sample size increases,the distribution of sample means of samples of size n (when randomly selected)approaches a normal distribution" is a fundamental assumption of the central-limit theorem.

Answer 1

True

Question 2

The primary purpose of inferential statistics is to make a judgment about a population.

Answer 2

True

Question 3

The average deviation score is frequently used in marketing research studies.

Answer 3

False
It is never used.Positive deviation scores are canceled out by negative scores,leaving an average deviation value of zero no matter how wide the spread may be.

Question 4

A common practice in marketing research is to use the 75 percent confidence interval about the mean in research studies.

Question 5

The normal distribution is represented by the normal curve.

Question 6

The Statistical Abstract of the United States which is published each year by the federal government is an example of descriptive statistics.

Question 7

A confidence interval estimate is a specified range of numbers within which a population mean is expected to lie.

Question 8

One hundred percent of the scores in a normal distribution fall within plus or minus two standard deviations of the mean.

Question 9

A cross reference is an estimate of the population mean in the form of a single value.

Question 10

The mean is simply the arithmetic average.

Question 11

The standardized normal distribution has a mean of 1.0 and a standard deviation of zero.

Question 12

The mode is the measure of central tendency that identifies the value that occurs most often.

Question 13

The standardized normal distribution is a purely theoretical probability distribution and is of little use in inferential statistics.

Question 14

If between 125 and 150 units of a product have been produced each day during the past month,the range of this production is 25 units.

Question 15

A frequency distribution of a sample is called a sample distribution.

Question 16

Percentage frequency is the long-run relative frequency with which an event will occur.

Question 17

A top box score generally refers to the portion of respondents who choose the most favorable response toward a company.

Question 18

The midpoint of a distribution,above which and below which half of the scores fall,is called the mode.

Question 19

Population parameters are computed from sample data.

Question 20

The standardized value of Z is computed by the formula: Z = (X - m)/s.

Question 21

The confidence interval increases as the sample size,n,increases.

Question 22

Three factors are required to specify sample size: (1)the variance of the population;(2)the population mean;and (3)the confidence level.

Question 23

Increases in sample size reduce sampling error at a decreasing rate.

Question 24

If the average units produced in a month by a Ford Motor Co.plant for Ford Explorers is 22,but only 18 Explorers are produced on a given day in that same month,the deviation score for this one day is:

A)+4
B)-4
C)40
D)2

Question 25

Which of the following is a measure of the central tendency of a set of scores?

A)mode
B)median
C)mean
D)all of the above

Question 26

The formula below is used to calculate the ____.

A)mode of a sample
B)median of a sample
C)sample mean
D)range of a sample

Question 27

When a researcher wants to estimate national market share based on the results of the test market for a new product in St.Louis and Kansas City,this is an example of:

A)descriptive statistics
B)the central limit theorem
C)inferential statistics
D)the standardized normal distribution

Question 28

Nicole has developed a set of data organized by summarizing the number of times a particular value of a variable occurs.This is an example of a:

A)population parameter
B)mean
C)frequency distribution
D)median

Question 29

The value below which half the values in a distribution fall is the ____.

A)mean
B)median
C)mode
D)range

Question 30

Which of the following refers to the proportion of respondents who choose the most positive choice in a multiple choice question?

A)heteroskedasticity
B)mode
C)median
D)top-box score

Question 31

Which of the following is a measure of dispersion?

A)mean
B)proportion
C)range
D)all of the above

Question 32

If the price of CD players in Denver range from $59 to $179,the range of these prices is:

A)$238
B)$3.03
C)$120
D)$179

Question 33

The arithmetic average of a set of numbers is referred to as the _____.

A)proportion
B)mode
C)mean
D)median

Question 34

The measure of central tendency that identifies the value that occurs most often is called the:

A)mean
B)median
C)mode
D)range

Question 35

A researcher must calculate the sample mean to calculate the confidence intervals.

Question 36

Find the mean score of the following set of scores: 2,5,7,4,8 .

A)4.8
B)5.2
C)7
D)26

Question 37

____ is the long-run relative frequency with which an event will occur.

A)Probability
B)Central tendency
C)Estimation
D)Deviation

Question 38

In most cases,the size of the population does not have a major effect on the sample size.

Question 39

If 206 people in a sample of 560 people say that they "liked a product" that they purchased during a test market study in Cincinnati,the proportion of people in this study who said that they liked this product was about:

A).40
B).37
C).56
D)2.71

Question 40

Measures computed from sample data are called:

A)sample statistics
B)population parameters
C)sample frequencies
D)normalized scores

Question 41

The formula below is used to calculate the ____.
(ZS/E)²

A)sample standard deviation
B)population standard deviation
C)sample size
D)sample variance

Question 42

The confidence interval for a proportion uses the following formula:

Question 43

One of the most common probability distributions in statistics is the _____ distribution.

A)normal
B)standard
C)central
D)confidence interval

Question 44

The formula below is the formula for the ____.

A)standard deviation
B)standard error of the mean
C)standard error of the proportion
D)variance

Question 45

In statistical terms,____ the sample size ____ the width of the confidence interval about the mean at a given confidence level.

A)increasing;decreases
B)increasing;increases
C)decreasing;decreases
D)none of the above

Question 46

All of the following are characteristics of the standardized normal distribution EXCEPT:

A)symmetrical about its mean
B)has an infinite number of cases
C)mean identifies the normal curve's highest point (the mode)
D)has a mean of 1 and a standard deviation of 0

Question 47

If the sample standard deviation is 10.5 and the sample mean is 48 based on a study with a sample size of 120,the 95 percent confidence interval about the mean is between approximately:

A)44.37 and 51.63
B)46.12 and 49.88
C)47.88 and 48.12
D)40.0 and 50.0

Question 48

Which theory states that as sample size increases,the distribution of sample means of size n,randomly selected,approaches a normal distribution?

A)prospect theory
B)central-limit theorem
C)dispersion theory
D)entropy

Question 49

A frequency distribution of the population elements is called a:

A)normal distribution
B)sample statistic
C)population distribution
D)standard error

Question 50

The following formula is the formula for calculating the ____.

A)standard error of the mean
B)standard deviation
C)standard normal distribution
D)variance

Question 51

An estimate of the population mean in the form of a single value,usually the sample mean,is called a:

A)confidence interval estimate
B)standard deviation
C)point estimate
D)variant

Question 52

Which of the following is the symbol for the sample standard deviation?

A)S
B)μ₂
C)σ
D)σ₂

Question 53

Which of the following represents the standard deviation of the sampling distribution?

A)range
B)standard median
C)dispersion
D)standard error of the mean

Question 54

Which of the following is a step in determining sample size?

A)estimate the standard deviation of the population
B)make a judgment about the allowable magnitude of error
C)determine a confidence level
D)all of the above

Question 55

If 35 percent of TV viewers recalled seeing an ad for a Ford Explorer on a particular television program based on a sample of 800 viewers,the 95 percent confidence interval for this study would be between approximately:

A)30 percent and 40 percent
B)32 percent and 38 percent
C)28 percent and 42 percent
D)20 percent and 30 percent

Question 56

If a researcher wants to study the impact of a price change in each of three regions of the U.S.(Eastern,Midwestern,and Western),the researcher should have a sample size of retailers in each region of at least ____ stores.

A)30
B)40
C)100
D)1000

Question 57

If the population mean is assumed to be 20 and the sample standard deviation is 5,a score of 15 would have a Z-value of approximately:

A)+1.00
B)-7.00
C)-1.00
D)+5.00

Question 58

Find the approximate standard deviation of the following set of scores: 3,6,2,7,8 .

A)2.24
B)2.59
C)3.32
D)6.70

Question 59

Which of the following is the symbol for the population standard deviation?

A)S
B)σ
C)μ
D)S²

Question 60

Which of the following eliminates the drawback of having the measure of dispersion in squared units rather than in the original measurement units?

A)standard deviation
B)variance
C)deviation
D)mean

Question 61

The idea that as sample size increases,the distribution of sample means of samples of size n,when randomly selected,approaches a normal distribution is known as the ____________________.

Question 62

When you add up a set of scores and divide the result by the number of scores,you have determined the ____________________ of the distribution.

Question 63

Explain the central-limit theorem and discuss why it is useful to marketing researchers.

Question 64

An estimate of the population mean in the form of a single value is called a(n)____________________.

Question 65

Name and describe the measures of central tendency.

Question 66

The percentage of elements that meet some criterion is referred to as the ____________________.

Question 67

The simplest measure of the dispersion of a set of scores is the ____________________.

Question 68

Discuss the three factors required to specify sample size.

Question 69

Measured characteristics of a specific population are called ____________________.

Question 70

When a data set is summarized by counting the number of times each value for a variable occurs in the sample,this is known as a ____________________.

Question 71

The middle score in the rank order of scores is called the ____________________ score.

Question 72

The ____________________ distribution is bell shaped.

Question 73

A frequency distribution organized into a table or graph that summarizes percentage values associated with particular values of a variable is called a(n)____________________.

Question 74

List the characteristics of the standardized normal distribution and explain why it is a useful distribution in inferential statistics.

Question 75

The range of numbers within which the population mean is expected to lie 95 percent of the time is known as the ____________________ estimate.

Question 76

The standard deviation of the sampling distribution is called the ____________________ of the mean.

Question 77

Describe the measures of dispersion and explain why standard deviation is used most often.

Question 78

Traditionally,market researchers have used the ____________________ percent confidence level in research studies.

Question 79

A frequency distribution of a sample is called a(n)____________________.

Question 80

In computing a 95 percent confidence interval about a proportion for a sample size of 40,the appropriate Z-value to be used is ____________________.