Deck 22: Bivariate Statistical Analysis: Differences Between Two Variables

Question 1

The independent samples t-test tests the differences between means taken from two independent samples or groups.

Answer 1

True

Question 2

The chi-square test requires that the expected frequency in each cell of the contingency table be at least 30.

Answer 2

False
The expected frequency in each cell should be at least 5.

Question 3

A pooled estimate of the standard error is a poorer estimate of the standard error than one based on the variance from either sample.

Answer 3

False
A pooled estimate of the standard error is a better estimate.

Question 4

When the difference between two groups is measured,this is a form of bivariate statistics.

Question 5

To use the chi-square test,both variables in a 2 x 2 contingency table must be measured on a ratio scale.

Question 6

In practice,t-test results are commonly calculated by hand because they are so simple.

Question 7

A t-test is not appropriate and should not be used when the sample size is greater than 30.

Question 8

The chi-square test tests the significance of the data in an R X C contingency table in which R stands for row and C stands for column.

Question 9

The degrees of freedom are calculated asd.f.= n - 1 when using the t-test for comparing two means.

Question 10

The t-test assumes that the two population variances are equal.

Question 11

The t-test for comparing the means of two groups assumes that the data are in nominal scales.

Question 12

A statistical test that is used often in marketing research tests the difference between two groups in terms of some behavior (e.g.attitude toward a brand).

Question 13

One way to test the significance of contingency tables is by means of the chi-square test.

Question 14

A cross-tabulation is a simple way to describe the relationships between two groups.

Question 15

The chi-square test requires the researcher to compare the observed frequencies of the groups with the expected frequencies of the groups.

Question 16

If a researcher is interested in whether adult males purchase a product more frequently than adult females,this is an example of univariate statistics.

Question 17

When no direction of a relationship is stated in the hypothesis,a one-tailed test is appropriate.

Question 18

Marketing researchers frequently use cross-tabulation techniques in data analysis.

Question 19

The first basic step in interpreting t-test results is to find the p-value associated with a particular t and the corresponding degrees of freedom.

Question 20

Means that appear to be not so close to each other are usually statistically concluded that they are different.

Question 21

A researcher hypothesizes that males and females differ with respect to attitude toward sports sponsorships.To investigate this hypothesis that these two groups' attitudes differ,he will use a:

A)bivariate test of differences
B)univariate test of differences
C)multivariate test of differences
D)cluster analysis

Question 22

In using the t-test to compare the means of two groups,the alternative hypothesis is typically stated as:

Question 23

In comparing the difference of the means between two groups,the null hypothesis can also be stated as:

Question 24

The total mean is the mean of a variable over all observations.

Question 25

In using the t-test to compare the means of two groups,the degrees of freedom are:

A)n₁ - n₂ - 2
B)n₁ + n₂ - 2
C)n₁ x n₂ -2
D)n₁ / n₂ - 2

Question 26

The formula for the chi-square test uses:

A)observed and expected frequencies
B)observed and expected percentages
C)the two sample means
D)the two sample standard deviations

Question 27

Supposed you used a 10-point rating scale to measure intention-to-buy (1 = definitely would not buy and 10 = definitely would buy).If a group of 40 males had a mean of 7 and a standard deviation of 2.5,while a group of 35 females had a mean of 5 and a standard deviation of 1.4,the standard error of the difference between the means would be approximately:

A)0.48
B)1.36
C)2.45
D)not enough information to determine

Question 28

In a brand awareness study,if 25 of a group of 35 males identify the brand correctly and 15 of a group of 35 females identify this brand correctly,the chi-square value for this study is approximately:

A)3.26
B)4.15
C)5.84
D)2.92

Question 29

Another form of the alternative hypothesis when testing the difference between the means of the two groups is:

Question 30

Another name for a cross-tabulation is:

A)ANOVA
B)Z-test
C)contingency table
D)between-group variance

Question 31

How many degrees of freedom are there in a four-cell chi-square test?

A)(R + 1)
B)(R - 1)
C)(R - 1)(C - 1)
D)R(C - 1)

Question 32

In order to use the chi-square test,the expected frequency in each of the cells of the contingency table should be at least:

A)2
B)5
C)30
D)40

Question 33

The F-test partitions the total variance into within-group variance and between-group variance.

Question 34

A Z-test for differences of proportions requires a sample size greater than 100.

Question 35

Suppose that you used a 9-point rating scale and that you wanted to compare men who had an annual income over $50,000 (Group 1)with men who had an annual income less than or equal to $50,000 (Group 2)on their liking of a new product.If you studied 40 men in Group 1 and they have a mean of 7 and a standard deviation of 2.5,while the 35 men in Group 2 have a mean of 5 and a standard deviation of 1.4,what is the approximate value of t using the t-test?

A)3.43
B)4.19
C)2.64
D)not enough information to determine

Question 36

The formula given below represents the method for calculating the:

A)Z-test
B)F-test
C)X² test
D)a

Question 37

If 25 of the 35 females in a research study agree with a statement,and 15 of the 35 males agree with this statement,the expected value for males-agree is:

A)15
B)20
C)25
D)35

Question 38

The null hypothesis for an ANOVA test comparing the means of three groups is: m₁ ₌ m₂ ₌ m₃.

Question 39

If the critical value of chi-square in the chi-square table is 3.84,and the obtained value of chi-square in the study is 3.45,the researcher should:

A)reject the null hypothesis
B)accept the null hypothesis
C)accept the research hypothesis
D)reject both the null and the research hypotheses

Question 40

A redundant-sample t-test is an appropriate test for comparing the scores of two interval drawn from related populations.

Question 41

In an ANOVA test of the differences between the means of three groups,the null hypothesis is:

Question 42

In a study comparing the means of two groups in which there are 45 males in Group 1 and 37 females in Group 2,the degrees of freedom for this study when using the t-test for the difference between means is:

A)84
B)80
C)82
D)160

Question 43

When a researcher needs to compare means for a variable grouped into two categories based on some less-than interval variable,a(n)____________________ test is appropriate.

Question 44

In practice,what is the first step in interpreting the t-test when comparing two means?

A)compute the t-test value
B)find the p-value associated with the t and the corresponding degrees of freedom
C)examine the difference in means to find the "direction" of any difference
D)examine if there is a difference at the 50 percent confidence interval before examining the 95 percent confidence interval

Question 45

The ____________________ test studies the significance of a joint frequency distribution.

Question 46

The F-distribution is a function of:

A)SSB - SSE
B)SSE - SSB
C)SSB/SSE
D)SSE/SSB

Question 47

Practically speaking,what is the first thing a researcher should do when interpreting ANOVA results?

A)examine the actual means for each group
B)determine the between-groups variance
C)examine the total variance
D)check whether or not the overall model F is significant

Question 48

When two variables are studied simultaneously in a research study,this is called ____________________ statistical analysis.

Question 49

In using the Z-test for comparing two proportions,the null hypothesis is typically stated as:

Question 50

The mean of a variable over all observations is called the:

A)master mean
B)average mean
C)grand mean
D)ANOVA mean

Question 51

Which test should be used when comparing the means of three groups to see if they are significantly different from one another?

A)One-group t-test
B)ANOVA test
C)Two-group t-test
D)Chi-square test

Question 52

Which test is appropriate for comparing the scores of two interval variables drawn from related populations?

A)ANOVA
B)relative t-test
C)relative x² test
D)pair-samples t-test

Question 53

The sum of the differences between observed values and the group mean for a given set of observations is known as the:

A)within-group error
B)between-groups variance
C)F-ratio
D)γ statistic

Question 54

Which of the following is the sum of differences between the group mean and the grand mean summed over all groups for a given set of observations?

A)between-groups variance
B)total error variance
C)F-statistic
D)X² value

Question 55

The key statistical test for an ANOVA model is the:

A)X² test
B)t-test
C)F-test
D)Z-test

Question 56

Suppose that you wanted to determine if the males in your sales force differed from the females in your sales force in the proportion of sales that they made to mass merchandiser chains.Your data show that the 80 males had 40% of their sales to these chains,while the 60 females had 25% of their sales to these chains.For these data,the standard error of the difference in proportions is approximately:

A)0.08
B)0.15
C)0.02
D)1.67

Question 57

A test of a hypothesis to determine if two groups differ with respect to the scores on one variable is called a(n)____________________.

Question 58

The alternative hypothesis when using the Z-test for the difference between the proportions for two groups is:

Question 59

In using the Z-test for comparing two proportions,if the pooled estimate of the proportion of successes is 0.36,then the pooled estimate of proportion of failures is:

A)1
B)0.36
C)0.64
D)0.13

Question 60

The formula for determining the degrees of freedom for a chi-square test is ____________________.

Question 61

An appropriate test for comparing the scores of two interval variables drawn from related populations is the ____________________.

Question 62

Explain what an independent samples t-test is and the null hypothesis examined.

Question 63

The statistical test that is used to compare the sample variance with another sample variance is the ____________________.

Question 64

List the practical steps for interpreting t-test results.

Question 65

Discuss when a paired-samples t-test is appropriate and give an example of when it should be used.

Question 66

What is ANOVA and when is it the appropriate statistical technique? What test is used to determine significance?

Question 67

One way to interpret the meaning of the results of the t-test is to focus on the ____________________ and the group means.

Question 68

The F-test partitions total variance into ____________________ variance and ____________________ variance.

Question 69

The ____________________ is the mean of a variable over all observations.

Question 70

Explain what a Z-test for comparing two proportions is and the appropriate null hypothesis.

Question 71

In using the t-test to compare the difference between the means of two groups,the null hypothesis is normally stated as ____________________.

Question 72

The sum of differences between the group mean and the grand mean summed over all groups for a given set of observations is called ____________________.

Question 73

____________________ is the appropriate test to use when comparing the means of three or more groups to see if they are significantly different from one another.

Question 74

In using the t-test to compare the difference between the means of two groups,the formula for determining the degrees of freedom is ____________________.

Question 75

The null hypothesis when using the Z-test for the differences between the proportions of two groups is that ____________________.