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

Question 1

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

Answer 1

True

Question 2

The standard deviation eliminates the drawback of having the measure of dispersion in squared units rather than the original measurement units.

Answer 2

True

Question 3

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

Answer 3

False

Question 4

The normal distribution is represented by the normal curve.

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

"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.

Question 10

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

Question 11

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

Question 12

The mean is simply the arithmetic average.

Question 13

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

Question 14

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

Question 15

Population parameters are measured characteristics of a specific population.

Question 16

A frequency distribution is a set of data organized by summarizing the number of times a particular value of a variable occurs.

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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

Question 22

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

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

Question 23

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

Question 24

Measures computed from sample data are called _____.

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

Question 25

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

Question 26

All of the following are measures of central tendency EXCEPT _____.

A) mode
B) standard deviation
C) median
D) mean

Question 27

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

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

Question 28

Find the median of the following scores: 1, 2, 3, 4, 5, 5, 7

A) 3.86
B) 4
C) 6
D) 27

Question 29

A set of data organized by summarizing the number of times a particular value of a variable occurs is referred to as a(n) _____.

A) inference table
B) frequency distribution
C) probability sample
D) sample summary

Question 30

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) 0.40
B) 0.37
C) 0.56
D) 2.71

Question 31

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

Question 32

The variance, or heterogeneity, of the population refers to the standard deviation of the population.

Question 33

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 these choices

Question 34

Hank has developed a set of data organized by summarizing the values resulting from rolling a pair of die. He constructed a table of his data and found that five was the most common result. This is an example of a _____.

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

Question 35

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 36

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 37

The percentage of elements that meet some criterion is called a(n) _____.

A) top-box score
B) distribution
C) proportion
D) range

Question 38

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

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

Question 39

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 40

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 41

A frequency distribution of the population elements is called a _____.

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

Question 42

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) mode identifies the normal curve's highest point
D) has a mean of 1 and a standard deviation of 0

Question 43

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 44

Which of the following is a measure of dispersion?

A) mean
B) proportion
C) range
D) all of these choices

Question 45

The _____ distribution is a symmetrical, bell-shaped distribution that describes the expected probability distribution of many chance occurrences.

A) bell-weather
B) common
C) normal
D) unique

Question 46

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 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

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

A) sample distribution
B) inferred distribution
C) secondary distribution
D) standard distribution

Question 49

Find the mode of the following scores: 1, 2, 3, 4, 5, 5, 7

A) 3.86
B) 4
C) 5
D) 6

Question 50

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

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

Question 51

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

A) S
B) s
C) m
D) S²

Question 52

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 53

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

A) S
B) m₂
C) s
D) s₂

Question 54

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 55

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 56

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 _____.

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

Question 57

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 58

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 59

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 60

If the price of a product ranges from $59 to $179, the range of these prices is _____

A) $238
B) $60
C) $120
D) $179

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

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

Question 63

A frequency distribution of the population elements is called a(n) _____ distribution.

Question 64

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 65

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 66

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

Question 67

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

Question 68

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

Question 69

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 these choices

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(n) ______.

Question 71

A specified range of numbers within which a population mean is expected to lie is known as the ______ estimate.

Question 72

If 35 percent of TV viewers recalled seeing an ad for a Toyota Prius 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 73

Three factors in determining sample size for questions involving means are: (1) the variance, or heterogeneity, of the population; (2) the magnitude of acceptable error; and (3) the _____.

Question 74

The confidence interval for a proportion uses which of the following formulas?

A) p $\pm$ ZS_p
B) S_p $\pm$ ZP
C) $\pm$ ZS_s
D) none of these choices

Question 75

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

Question 76

When you add up a set of scores and divide the result by the number of scores, you have determined the ______ of the distribution, which is a measure of central tendency.

Question 77

Variables in a sample or measures computed from sample data are called _____.

Question 78

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

Question 79

The _____ distribution is bell shaped.

Question 80

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 these choices