Deck 22: Bivariate Statistical Analysis: Differences Between Two Variables

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

In practice, computer software is used to compute the t-test results.

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

The type of measurement, the nature of the comparison, and the number of groups to be compared influence the statistical choice.

Question 9

If a researcher is interested in whether males switch jobs more frequently than do females, this is an example of univariate statistics.

Question 10

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

Question 11

Tests are bivariate tests of differences when they involve only two variables: a variable that acts like a dependent variable and a variable that acts as a classification variable.

Question 12

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

Question 13

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

Question 14

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 15

The reason that means that appear to be not so close could be concluded to be statistically the same is due to the variance.

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

ANOVA involving only one grouping variable is often referred to as one-way ANOVA.

Question 22

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 23

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 24

A(n) _____ is a test for hypotheses stating that the mean scores from some interval- or ratio-scaled variable group based on some less-than interval classificatory variable are not the same.

A) regression
B) cluster analysis
C) c² test
D) independent samples t-test

Question 25

The null hypothesis for an ANOVA test comparing the means of three groups is: m_{1 ¹} m_{2 ¹} m_3.

Question 26

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 27

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

Question 28

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 29

The formula given below represents the method for calculating the _____.

A) Z-test
B) F-test
C) c² test
D) a

Question 30

how do you determine the degrees of freedom in a four-cell chi-square test?

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

Question 31

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 32

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 33

In using the t-test to compare the means of two groups, the degrees of freedom are calculated as _____.

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

Question 34

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 35

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 36

Total variability is the calculated by dividing the within-group variance by the between-group variance.

Question 37

A _____ is an investigation of a hypothesis stating that two (or more) groups differ with respect to measures on a variable.

A) statistical conclusions
B) descriptive analysis
C) paired comparison
D) test of differences

Question 38

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

A) p-test
B) t-test
C) c² test
D) univariate test

Question 39

All of the following are true regarding cross-tabulation EXCEPT _____.

A) The c² distribution provides a means for testing the statistical significance of a contingency table.
B) The c² for a contingency table compares two means that are not from independent samples.
C) Cross-tabulations are much like tallying.
D) The c² test for a contingency table involves comparing the observed frequencies with the expected frequencies in each cell of the table.

Question 40

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

Question 41

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) g statistic

Question 42

Which of the following is a requirement for using the Z-test for differences of proportions?

A) common sample
B) degrees of freedom of at least 50
C) sample size greater than 30
D) ratio measurement of all variables

Question 43

_____ involves the investigation of the effects of one treatment variable on an interval-scaled dependent variable and determines whether statistically significant differences in means occur between two or more groups.

A) Analysis of variance (ANOVA)
B) Regression analysis
C) Cross-tabulation
D) c²

Question 44

Proper use of the c² test requires that each expected frequency have a value of at least _____.

Question 45

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 46

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 47

The key statistical test for an ANOVA model is the _____.

A) c² test
B) t-test
C) F-test
D) Z-test

Question 48

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

Question 49

The mean of a variable over all observations is called the _____.

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

Question 50

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

A) m_{1 =} m_{2 =} m₃
B) m₁ ¹ m₂ ¹ m₃
C) m₁ - m₂ - m_{3 =} 0
D) m₁ + m₂ + m_{3 =} 1

Question 51

The F-distribution is a function of _____.

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

Question 52

Which 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
C) Three-group t-test
D) Chi-square test

Question 53

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 54

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 55

The Z-test for comparing two proportions is appropriate with which null hypothesis (H₀)?

A) p₁ = p_2.
B) p₁ ¹ p_2.
C) p₁ x p₂ = 1
D) p₁ - p₂ = 1

Question 56

The ______ test studies the significance of a contingency table.

Question 57

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) c² value

Question 58

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

Question 59

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

A) ANOVA
B) relative t-test
C) relative c² test
D) pair-samples t-test

Question 60

All of the following are forms of variance considered in an F-test EXCEPT _____.

A) SSE
B) SSB
C) SSR
D) SST

Question 61

A researcher has data on viewers' responses regarding what company sponsored the Super Bowl half-time show for the past two years and has coded it "1" if the response was correct and "0" if not. He would like to examine if there is a statistical difference in correct answers between the two years. Explain what statistical test is appropriate to address this research question.

Question 62

Discuss the factors that influence the statistical choice. If a researcher is examining factors that influence an automobile's gas mileage, which statistical tool (or tools) is appropriate?

Question 63

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

Question 64

What is ANOVA and when is it the appropriate statistical technique? What test is used to determine significance? Give an example of a research question that can be analyzed using ANOVA.

Question 65

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

Question 66

The _____ for differences of proportions is a technique used to test the hypothesis that proportions are significantly different for two independent samples or groups.

Question 67

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

Question 68

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

Question 69

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

Question 70

List the practical steps for interpreting t-test results.

Question 71

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 72

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

Question 73

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

Question 74

The _____ is an estimate of the standard error for a t-test of independent means that assumes the variances of both groups are equal.

Question 75

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

Question 76

The statistical test for an ANOVA model is the ______.

Question 77

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