Deck 15: Frequency Distribution, Crosstabulation, and Hypothesis

Question 1

The alternative hypothesis: the percentage of Internet users who use the Internet for shopping is greater than .40, is a .

A) two- tailed test
B) Type II error
C) Type I error
D) one- tailed test

Answer 1

D

Question 2

are hypothesis testing procedures that assume that the variables are measured on a nominal or ordinal scale.

A) Nonparametric tests
B) Parametric tests
C) Parameter tests
D) None of the above

Answer 2

A

Question 3

Which of the following statements is not true concerning cross- tabulation?

A) Cross- tabulation examines association between variables, not causation.
B) No more than three variables can be cross- tabulated.
C) As a general rule, there should be at least five expected observations in each cell for the statistics computed to be reliable.
D) None of the above statements is untrue.

Answer 3

B

Question 4

Which statement is not correct about cross- tabulations?

A) Cross- tabulation tables are also called contingency tables.
B) Cross- tabulations provide inferences for making statements about the means of parent populations.
C) The margins of a cross- tabulation show the same information as the frequency tables for each of the variables.
D) The data are considered to be qualitative or categorical data.

Question 5

The test is a nonparametric test for examining differences in the location of two populations, based on paired observations, that compares only the signs of the differences between pairs of variables without taking into account the magnitude of the differences.

A) runs test
B) sign test
C) binomial test
D) Mann- Whitney U test

Question 6

is a modified version of the phi correlation coefficient, 0.

A) Cramer's V
B) Chi- square statistic
C) Asymmetric lambda
D) Coefficient of variation

Question 7

occurs when the sample results lead to the rejection of a null hypothesis that is in fact true.

A) Two- tailed error
B) Type I error
C) Type II error
D) One- tailed error

Question 8

If the probability of F is greater than the significance level a, and should be used.

A) H₀ is rejected; t based on "equal variances assumed"
B) H₀ is not rejected; t based on "equal variances not assumed"
C) H₀ is rejected; t based on "equal variances not assumed"
D) H₀ is not rejected; t based on "equal variances assumed"

Question 9

The square root of the variance is the .

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

Question 10

Which of the following statements is true concerning cross- tabulations with two variables?

A) Because two variables have been cross- classified, percentages could be computed either column- wise, based on column totals, or row- wise, based on row totals.
B) Cross- tabulation with two variables is also known as bivariate cross- tabulation.
C) The general rule is to compute the percentages in the direction of the independent variable, across the dependent variable.
D) All of the above statements are true.

Question 11

The degrees of freedom for the t statistic to test hypotheses about one mean are .

A) n - 1
B) n₁ + n₂ C) n
D) n₁ +n₂ - 2

Question 12

is a measure of the strength of association used in tables larger than 2 × 2.

A) Cramer's V
B) Coefficient of variation
C) Chi- square coefficient
D) Phi coefficient

Question 13

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

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

Question 14

Which of the following statements is not true about parametric tests?

A) The t statistic assumes that the variable is normally distributed and the mean is known (or assumed to be known) and the population variance is estimated from the sample.
B) Parametric tests are used when the independent variables are non- metric.
C) The t test is a commonly used parametric test.
D) B and C are not correct.

Question 15

The is the value that occurs most frequently.

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

Question 16

The introduction of a third variable in cross- tabulation can result in which of the following possibilities?

A) no change in the initial pattern
B) refined association between the two original variables
C) no association between the two original variables
D) All of the above are correct.

Question 17

Which statement is not related to statistics associated with cross- tabulation?

A) The t test could be conducted on the mean of one sample or two samples of observations.
B) Generally, the strength of association is of interest only if the association is statistically significant.
C) The strength of association can be measured by the phi correlation coefficient, the contingency coefficient, Cramer's V, and the lambda coefficient.
D) The statistical significance of the observed association is commonly measured by the chi- square statistic.

Question 18

is a measure of the relative peakedness or flatness of the curve defined by the frequency distribution.

A) Type II error
B) Type I error
C) Kurtosis
D) Skewness

Question 19

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

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

Question 20

A frequency distribution helps determine .

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

Question 21

Which statement is not correct about the null hypothesis?

A) Accepting the null hypothesis will lead to some changes in opinions or action.
B) In marketing research, the null hypothesis is formulated in such a way that rejection leads to the acceptance of the desired conclusion.
C) It is always the hypothesis tested.
D) It can never be accepted based on a single statistical test.

Question 22

For the parametric case involving the means of paired samples, the null and alternative hypotheses are .

A) H₀: a₁² = a₂² H₁: a₁² × a₂²

Question 23

When the difference in the location of two populations is to be compared based on observations from two independent samples, and the variable is measured on an ordinal scale, the can be used.

A) binomial test
B) Mann- Whitney U test
C) Kolmogorov- Smirnov one- sample test
D) runs test

Question 24

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

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

Question 25

A frequency distribution helps .

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

Question 26

To balance the two types of errors, alpha (a), also known as _ , is often set at .01 or .05.

A) level of significance
B) Type I error
C) Type II error
D) A and B are correct

Question 27

The is a symmetric bell- shaped distribution that is useful for small sample (n < 30) testing.

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

Question 28

Which of the research questions/hypotheses below is best answered using hypothesis testing?

A) Is familiarity with a new product related to age and education levels after controlling for income?
B) One hotel has a more upscale image than its close competitor.
C) The department store is being patronized by more than 10 percent of households.
D) Both B and C are correct.

Question 29

The can be used to assess the strength of association in a table of any size.

A) contingency coefficient
B) chi- square coefficient
C) coefficient of variation
D) phi coefficient

Question 30

is a test statistic that measures the association between two ordinal- level variables. It makes an adjustment for ties and is most appropriate when the table of variables is not square but a rectangle.

A) Gamma
B) Symmetric lambda
C) Tau c
D) Tau b

Question 31

If the population standard deviation was assumed to be known, rather than estimated from the sample, a would be appropriate rather than a(n) .

A) z test; F test
B) t test; F test
C) z test; t test
D) t test; z test

Question 32

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

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

Question 33

is a test statistic that measures the association between two ordinal- level variables. It does not make an adjustment for ties.

A) Tau b
B) Gamma
C) Tau c
D) Symmetric lambda

Question 34

In the context of the Internet usage example, suppose we wanted to test whether the probability of observing a K value of .222, as determined by the normalized z statistic, is 0.103. Because this is more than the significance level of 0.05, the null hypothesis cannot be rejected. What do the results mean?

A) The distribution of the Internet usage does deviate significantly from the normal distribution.
B) The proportion of users for males and for females is significantly different for the two samples.
C) The distribution of the Internet usage does not deviate significantly from the normal distribution.
D) The proportion of users for males and for females is not significantly different for the two samples.

Question 35

Which program or function listed below is not useful for conducting nonparametric tests?

A) NPAR TESTS
B) Stat>Time Series
C) NPAR1WAY
D) none of the above

Question 36

A statistical technique that describes two or more variables simultaneously and results in tables that reflect the joint distribution of two or more variables that have a limited number of categories or distinct values is a .

A) parametric test
B) cross- tabulation
C) non- parametric test
D) t test

Question 37

is a measure of the percentage improvement in predicting the value of the dependent variable, given the value of the independent variable in contingency table analysis.

A) Tau b
B) Tau c
C) Asymmetric lambda
D) Symmetric lambda

Question 38

Which of the following statements is not correct about the alternative hypothesis?

A) The alternative hypothesis is the opposite of the null hypothesis.
B) There is no way to determine whether the alternative hypothesis is true.
C) The alternative hypothesis represents the conclusion for which evidence is sought.
D) None of the statements is correct.

Question 39

Which of the research questions/hypotheses below is best answered using cross- tabulations?

A) The department store is being patronized by more than 10 percent of households.
B) Is familiarity with a new product related to age and education levels?
C) One hotel has a more upscale image than its close competitor.
D) Both B and C are correct.

Question 40

The F test of sample variance may be performed if it is not known whether the two populations have equal variance. In this case the hypotheses are .

A) H₀: µ₁ = µ₂ H₁: µ₁ × µ₂

Question 41

The test statistic used in the Kolmogorov- Smirnov one- sample test is .

A) K = Max lA_i - O_i l
B) K = Min lA_i - O_i l
C) K = Max l O_i, A_il
D) K = Min l O_i , A_i l

Question 42

The is a frequency distribution that depends upon two sets of degrees of freedom, the degrees of freedom in the numerator and the degrees of freedom in the denominator.

A) t distribution
B) chi- square distribution
C) Z statistic
D) none of the above

Question 43

The is a statistical test of the equality of the variances of two populations.

A) F test
B) z test
C) paired samples test
D) t test

Question 44

Which test is not an independent samples test?

A) Kolmogorov- Smirnov two- sample test
B) two- sample median test
C) Wilcoxon matched- pairs signed- ranks test
D) Mann- Whitney U test

Question 45

The test statistic used in the Wilcoxon matched- pairs signed- ranks test is .

A) z
B) chi- square
C) t
D) alpha

Question 46

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 47

Tau b, tau c, and gamma are available to measure association between two _ variables. - level

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

Question 48

Which of the following tests is not a non- parametric one- sample test?

A) Mann- Whitney U test
B) runs test
C) binomial test
D) Kolmogorov- Smirnov one- sample test

Question 49

The degrees of freedom for the t statistic to test the hypothesis about two independent samples is .

A) n
B) n₁ +n₂ - 2
C) n - 1
D) n₁ + n₂

Question 50

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) range
B) median
C) mean
D) mode

Question 51

Hypothesis tests can be related to _.

A) tests of strength
B) tests of association
C) tests of differences
D) B and C are correct

Question 52

Mean, median, variance, standard deviation, minimum, maximum, and range are some of the statistics that can be calculated via _, , and in SPSS.

A) FREQUENCIES; EXPLORE; DESCRIPTIVES
B) EXPLORE; DESCRIPTIVES; COUNTS
C) COUNTS; FREQUENCIES; DESCRIPTIVES
D) DESCRIPTIVES; COUNTS; EXPLORE

Question 53

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

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

Question 54

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

Question 55

Suppose we wanted to test the hypothesis that the mean familiarity rating exceeds 4.0, the neutral value on a seven- point scale. The hypotheses may be formulated as _ .

A) H₀: µ c 4.0 H₁: µ > 4.0

Question 56

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

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

Question 57

are hypothesis testing procedures that assume that the variables of interest are measured on at least an interval scale.

A) Parametric tests
B) Parameter tests
C) Nonparametric tests
D) None of the above

Question 58

A one- sample nonparametric goodness- of- fit test to determine whether the observations for a particular variable could reasonably have come from a particular distribution is the .

A) Mann- Whitney U test
B) Kolmogorov- Smirnov one- sample test
C) binomial test
D) runs test

Question 59

The is used to test the statistical significance of the observed association in cross- tabulation.

A) Cramer's V
B) chi- square statistic
C) contingency coefficient
D) phi coefficient

Question 60

If the samples used in the Mann- Whitney U test are from the same population, the distribution of scores from the two groups in the rank list should be .

A) random
B) uniform
C) u- shaped
D) normal

Question 61

The is the probability of rejecting the null hypothesis when it is in fact false, and should be rejected.

A) level of significance
B) power of a test
C) Type II error
D) Type I error

Question 62

In cross- tabs, the introduction of a third variable can .

A) indicate no change in the initial association
B) refine the association observed between the two original variables
C) indicate no association between the two variables, although an association was initially observed
D) All of the above are correct.

Question 63

is a test statistic that measures the association between two ordinal- level variables. It makes an adjustment for ties and is most appropriate when the table of variable is square.

A) Symmetric lambda
B) Tau c
C) Tau b
D) Gamma

Question 64

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

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

Question 65

The is a skewed distribution whose shape depends solely on the number of degrees of freedom. As the number of degrees of freedom increases, the distribution becomes more symmetrical.

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

Question 66

The is a statistic that assumes that the variable has a symmetric bell- shaped distribution and the mean is known (or assumed to be known) and the population variance is estimated from the sample.

A) z statistic
B) t statistic
C) F statistic
D) none of the above

Question 67

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

A) Type I error
B) skewness
C) Type II error
D) kurtosis

Question 68

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 69

A nonparametric test that analyzes the differences between the paired observations, taking into account the magnitude of the differences is the .

A) McNemar test
B) sign test
C) Wilcoxon matched- pairs signed- ranks test
D) runs test

Question 70

Also known as beta error, occurs when the sample results lead to the nonrejection of a null hypothesis that is in fact false.

A) Type II error
B) two- tailed error
C) one- tailed error
D) Type I error

Question 71

The is a univariate hypothesis test using the t distribution, which is used when the standard deviation is unknown and the sample size is small.

A) t test
B) paired samples test
C) F test
D) z test

Question 72

The is the ratio of the standard deviation to the mean, expressed as a percentage, and it is a unitless measure of relative variability.

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

Question 73

Which statement is not true concerning the t distribution?

A) Compared to the normal distribution, the t distribution has more area in the tails and less in the center.
B) As the number of degrees of freedom increases, the t distribution approaches the normal distribution.
C) The population variance is unknown and is estimated by the sample variance s².
D) The t distributions are skewed to the left.

Question 74

is an average of the two asymmetric lambda values. It does not make an assumption about which variable is dependent.

A) Tau b
B) Tau c
C) Symmetric lambda
D) Gamma

Question 75

A Kolmogorov- Smirnov one- sample test was conducted. The largest absolute difference between the observed and normal distribution was K = 0.222. The sample size was only 30 therefore, the approximate formula was used and the critical value for K was 0.248. Because the calculated value of K is than the critical value, the null hypothesis be rejected.

A) larger; can
B) larger; cannot
C) smaller; cannot
D) smaller; can

Question 76

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

A) binomial test
B) sign test
C) Mann- Whitney U test
D) runs test

Question 77

For the parametric case, involving proportions for two independent samples, the null and alternative hypotheses are .

A) H₀: a₁² = a₂² H₁: a₁² × a₂²

Question 78

The is used as a measure of the strength of association in the special case of a table with two rows and two columns (a 2 × 2 table).

A) Cramer's V
B) chi- square coefficient
C) contingency coefficient
D) phi coefficient

Question 79

Nonparametric tests are not available in .

A) Excel
B) SPSS
C) MINITAB
D) SAS

Question 80

In the parametric case of means for two independent samples, the hypotheses take which form?

A) H₀: a₁² = a₂² H₁: a₁² × a₂²