Deck 15: Frequency Distribution, Cross-Tabulation, and Hypothesis Testing

Question 1

The tendency of the deviations from the mean to be larger in one direction than in the other is called skewness.

Answer 1

True

Question 2

If all the data points are multiplied by a constant, the interquartile range is multiplied by the same constant.

Answer 2

True

Question 3

If a variable is measured on a nominal scale, the median should be used.

Answer 3

False

Question 4

Mean, median, and mode are measures of variability.

Question 5

The difference between the mean and an observed value is called the deviation from the mean.

Question 6

In a frequency distribution, two variables are considered at a time.

Question 7

The mode represents the highest peak of the distribution.

Question 8

The measures of location are also known as measures of central tendency because they tend to describe the center of the distribution.

Question 9

The variance can never be negative.

Question 10

Measures of location or central tendency include the mean, median, and mode.

Question 11

If the kurtosis is positive, the distribution is more peaked than a normal distribution.

Question 12

The mean is sensitive to extremely small or extremely large values (outliers).

Question 13

When calculating the standard deviation, we divide by n-1 because the sample is drawn from a population and we are trying to determine how much the responses vary from the mean of the entire population.

Question 14

The Range = X_Largest - X_Smallest.

Question 15

If the entire sample is changed by adding a fixed constant to each observation, then the mean, variance, and median change by the same fixed amount.

Question 16

In a symmetric distribution, the values on either side of the center of the distribution are the same, and the mean mode, and median are equal.

Question 17

The most commonly used statistics associated with frequencies are measures of location, measures of variability, and measures of occasion.

Question 18

The valid percentage column in a frequency distribution represents percentages calculated by excluding the cases with missing values.

Question 19

When the data points are scattered, variance is small.

Question 20

Frequency data may be used to construct a histogram, or a vertical bar chart.

Question 21

The alternative hypothesis is a statement that some difference or effect is expected.

Question 22

In commercial marketing research, the one-tailed test is used more often than a two-tailed test.

Question 23

Cross-tabulation examines associations between variables, not causation.

Question 24

If the calculated value of the test statistic is less than the critical value of the test statistic (TS _CR), the null hypothesis is rejected.

Question 25

The test statistic measures how close the sample has come to the null hypothesis and often follows a well-known distribution, such as the normal, t, or chi-square distribution.

Question 26

The first step in hypothesis testing is to select an appropriate statistical technique and the corresponding test statistic.

Question 27

A cross-tabulation is the merging of the frequency distribution of two or more variables in a single table to help us to understand how one variable relates to another variable.

Question 28

If the probability associated with the calculated or observed value of the test statistic (TS _CAL)is greater than the level of significance (α), the null hypothesis is rejected.

Question 29

Type I error occurs when the sample results lead to the rejection of the null hypothesis when it is in fact true.

Question 30

The probability of Type II error (α)is also called the level of significance.

Question 31

In cross-tabulation, the introduction of a third variable clarifies the initial association (or lack of it)observed between two variables and can result in six possibilities.

Question 32

The two-tailed test is more powerful than the one-tailed test.

Question 33

For a given level of α, increasing the sample size will decrease β, thereby increasing the power of the test.

Question 34

In tests of associations, the null hypothesis is that there is no association between the variables (H₀:......is NOT related to....).

Question 35

In tests of differences, the null hypothesis is that there is a difference (H₀:.....is different than....).

Question 36

In determining the critical value of the test statistic, the area to the right of the critical value is either α or α/2.It is α for a one-tail test and α/2 for a two-tail test.

Question 37

The null hypothesis is always the hypothesis that is tested.

Question 38

When using the chi-square statistic in cross-tabulation, the null hypothesis (H₀)will be rejected only when the calculated value of the test statistic is greater than the critical value of the chi-square distribution with the appropriate degrees of freedom.

Question 39

The null hypothesis, H₀, when using the chi-square statistic, is that there is no association between the variables.

Question 40

The null hypothesis refers to a specified value of the population parameter, not a sample statistic.

Question 41

The two-sample median test examines whether the two distributions are the same.

Question 42

The Mann-Whitney U test is a statistical test for a variable measured on an ordinal scale, comparing the difference in the location of two populations based on observations from two independent samples.

Question 43

The two-sample median test is not as powerful as the Mann-Whitney U test.

Question 44

When measuring the strength of association with the contingency coefficient, the maximum value of 1 is achieved when the variables are perfectly associated.

Question 45

The chi-square statistic can be estimated on counts of data or on percentages.

Question 46

The critical value of the F distribution depends upon two sets of degrees of freedom-those in the numerator and those in the denominator.

Question 47

The runs test tests the goodness of fit of the observed number of observations in each category to the number expected under specified binomial distribution.

Question 48

When conducting cross-tabulation analysis in practice, if H₀ is rejected, the pattern of the relationship should be interpreted by computing an appropriate statistic (phi coefficient, contingency, Cramer's V, lambda coefficient, or other statistics).

Question 49

The F static is computed as the ratio of two sample variances.

Question 50

Nonparametric tests are used when the independent variables are nonmetric.

Question 51

Hypothesis-testing procedures can be broadly classified as parameter or nonparameter based on the measurement scale of the variables involved.

Question 52

In the Mann-Whitney U test, two samples are combined and the cases are ranked in order of increasing size. The test statistic, U, is computed as the number of times a score from sample 1 or group 1 follows a score from group 2.

Question 53

The binomial test is a test of randomness for a dichotomous variable.

Question 54

An asymmetrical lambda value of 1 happens when each independent variable category is associated with a single category of the dependent variable.

Question 55

The Kolmogorov-Smirnov one-sample test is a goodness of fit test that compares the cumulative distribution function for a variable with a specified distribution.

Question 56

Paired samples are two samples that are not experimentally related.

Question 57

In hypothesis testing, the observations are paired so that the two sets of observations relate to the same respondents.

Question 58

The McNemar test is another paired sample nonparametric test that is used in the special case of a binary variable where the researcher wishes to test differences in proportions.

Question 59

Lambda assumes that the variables are measured on an ordinal scale.

Question 60

When variables are perfectly associated, the phi coefficient assumes the value of 1.

Question 61

The ________ is the difference between the 75th and 25th percentile.

A)standard deviation
B)coefficient of variation
C)variance
D)interquartile range

Question 62

In SPSS, if the data are interval scaled and only the summary statistics are desired, the DESCRIPTIVES procedure can be used.

Question 63

A frequency distribution helps ________.

A)determine how close a sample comes to the null hypothesis
B)us to understand how one variable, X, relates to another variable, Y
C)determine if a systematic association exists between two variables
D)determine the shape of the empirical distribution of the variable

Question 64

A frequency distribution helps determine ________.

A)the extent of nonresponse
B)the extent of illegitimate responses
C)the presence of outliers or cases with extreme values
D)all of the above

Question 65

As a general rule to follow to determine which of the different measures of location to use, if the variable is measured on a nominal scale, ________ is the appropriate measure of central tendency that should be used.

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

Question 66

The sign test is more powerful than the Wilcoxon matched-pairs signed-ranks test.

Question 67

Nonparametric tests are conducted in SPSS via the NONPARAMETRIC TESTS program.

Question 68

A statistic that describes a location within a data set is a ________.

A)measure of variability
B)measure of shapes
C)measure of occasion
D)measure of location

Question 69

The median is an appropriate measure of central tendency for ________ data.

A)interval
B)ratio
C)ordinal
D)nominal

Question 70

The value obtained by summing all elements in a set and dividing by the number of elements is the ________.

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

Question 71

The ________ is the most appropriate measure of central tendency for interval or ratio data.

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

Question 72

The difference between the smallest and the largest values in a distribution is the ________.

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

Question 73

________ include the range, interquartile range, variance or standard deviation, and coefficient of variation.

A)Measures of variability
B)Measures of shape
C)Measures of occasion
D)Measures of location

Question 74

A statistic that indicates the distribution's dispersion is a ________.

A)measure of variability
B)measure of shape
C)measure of occasion
D)measure of location

Question 75

Which of the research questions/hypotheses below is best answered using frequency distribution?

A)What percentage of the market consists of heavy users, medium users, light users, and nonusers?
B)The heavy and light users of a brand differ in terms of psychographic characteristics.
C)What is the income distribution of brand users? Is this distribution skewed toward low income brackets?
D)Both A and C are correct.

Question 76

The square root of the variance is the ________.

A)standard deviation
B)coefficient of variation
C)variance
D)interquartile range

Question 77

The ________ is the value that occurs most frequently.

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

Question 78

A measure of central tendency given as the value above which half of the values fall and below which half of the values fall is the ________.

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

Question 79

A mathematical distribution whose objective is to obtain a count of the number of responses associated with different values of one variable and to express these counts in percentage terms is a(n)________.

A)t distribution
B)frequency distribution
C)chi-square distribution
D)distribution

Question 80

The mean squared deviation of all the values from the mean is the ________.

A)standard deviation
B)coefficient of variation
C)variance
D)interquartile range