Question 1

Your research hypothesis is "In the population, the average number of days female unauthorized immigrants stay in the U.S. is longer than the average number of days male unauthorized immigrants stay in the U.S." What type of hypothesis test should be used?
A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Accepted Answer

An independent-samples t test should be used in this scenario as we are comparing the means of two independent groups (female and male unauthorized immigrants) to test if there is a significant difference between them.

Question 2

An author reports the following information about a one-way ANOVA: F = 0.95, df = 3 and 48, p = .231. Which of the following is true?
A) There were 3 groups being compared.
B) The null hypothesis was rejected
C) The sample results were not significant.
D) The post hoc multiple comparisons should be examined.

Accepted Answer

A non-significant p-value (greater than .05) indicates that the sample results were not significant and we fail to reject the null hypothesis. The degrees of freedom (df) suggest that there were 3 groups being compared, but no information is given about the null hypothesis or whether post hoc multiple comparisons were conducted.

Question 3

You are doing a one-way ANOVA. What level of measurement is required on the two variables you are using? (Circle the letter of the correct answer.)
A) Both must be interval ratio.
B) Both can be any level.
C) The dependent variable can be any level, the factor variable must be interval/ratio.
D) The dependent variable must be interval/ratio, the factor variable can be any level.

Accepted Answer

In a one-way ANOVA, the dependent variable must be at the interval or ratio level, while the factor (independent variable) is categorical.

Question 4

If race and gender have a significant interaction effect on years of schooling,
A) the effect of race on years of schooling varies by gender
B) the effect of gender on years of schooling varies by race
C) "a" and "b" are both true
D) none of the above are true

Accepted Answer

When there is a significant interaction effect between race and gender on years of schooling, it means that the effect of one variable on the outcome (years of schooling) depends on the level of the other variable. Thus, both options A and B are true: the effect of race on years of schooling varies by gender, and the effect of gender on years of schooling varies by race.

Question 5

Your research hypothesis is "In the population, there is a difference in the average number of work days per year lost due to injury among the following groups: secretaries, professors, police officers, and ministers." What type of hypothesis test should be used?
A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Accepted Answer

The correct test is one-way ANOVA because the hypothesis involves comparing the means of more than two independent groups to see if there is a significant difference among them.

Question 6

Your one-way ANOVA research hypothesis was that average years of schooling (EDUC) differed between strong Republicans, Independents, and strong Democrats. On the basis of the following output, which pairs of groups significantly differ?
Multiple Comparisons
EDUC Tukey HSD
$\begin{array}{|ll|r|r|r|}
\hline & & & & \
\text { (I) POLPARTY } & \text { (J) POLPARTY } & \begin{array}{c}
\text { Mean } \
\text { Difference (1- } \
\mathrm{J}
\end{array} & \text { Std. Error } & \text { Sig. } \
\hline 1 \text { strong Republican } & 4 \text { independent } & 1.647^{*} & .602 & .018 \
& 7 \text { strong Democrat } & -471 & .606 & .718 \
\hline 4 \text { independent } & 1 \text { strong Republican } & -1.647^{*} & .602 & .018 \
& 7 \text { strong Democrat } & -2.118^{*} & .511 & .000 \
\hline 7 \text { strong Democrat } & 1 \text { strong Republican } & 471 & .606 & .718 \
& 4 \text { independent } & 2.118^{*} & .511 & .000 \
\hline
\end{array}$
$*$. The mean difference is significant at the $0.05$ level.
A) no pairs significantly differ
B) (strong Republicans & strong Democrats)
C) (strong Republicans & Independents) and (Strong Democrats & Independents)
D) all pairs significantly differ

Accepted Answer

The significant differences are indicated by a Sig. value less than 0.05, which occurs between strong Republicans & Independents and between Strong Democrats & Independents.

Question 7

On the basis of this output, which of the following is true?
Tests of Between-Subjects Effects
Dependent Variable:INCOME
$\begin{array}{|l|r|r|r|r|r|}
\hline \text { Source } & {\begin{array}{c}
\text { Type III Sum } \
\text { of Squares }
\end{array}} & \text { df } & \text { Mean Square } & {\mathrm{F}} & {\text { Sig. }} \
\hline \text { Corrected Model } & 1.810 \mathrm{E} 10 & 5 & 3.619 \mathrm{E} 9 & 4.303 & .001 \
\text { Intercept } & 9.911 \mathrm{E} 10 & 1 & 9.911 \mathrm{E} 10 & 117.844 & .000 \
\text { MARRIED } & 6.674 \mathrm{E9} & 2 & 3.337 \mathrm{E9} & 3.967 & .021 \
\text { SEX } & 4.128 \mathrm{E9} & 1 & 4.128 \mathrm{E} 9 & 4.908 & .028 \
\text { MARRIED * SEX } & 1.308 \mathrm{E} 9 & 2 & 6.540 \mathrm{E} 8 & .778 & .461 \
\text { Error } & 1.354 \mathrm{E} 11 & 161 & 8.410 \mathrm{E} 8 & & \
\text { Total } & 3.156 \mathrm{E} 11 & 167 & & & \
\text { Corrected Total } & 1.535 \mathrm{E} 11 & 166 & & & \
\hline
\end{array}$
a. R Squared $= .118 ($ Adjusted R Squared $= .090 )$
A) The overall model is not significant.
B) The interaction effect is not significant.
C) The main effect of MARRIED is not significant.
D) The main effect of SEX is not significant.

Accepted Answer

The interaction effect between MARRIED and SEX (MARRIED * SEX) has a significance (Sig.) value of .461, which is greater than the common alpha level of .05, indicating that the interaction effect is not significant.

Question 8

You are doing a two-way ANOVA. What level of measurement is required for the dependent variable?
A) It must be nominal.
B) It must be ordinal.
C) It must be interval/ratio.
D) It can be any level of measurement.

Accepted Answer

A two-way ANOVA requires the dependent variable to have an interval/ratio level of measurement. This is because ANOVA tests the differences between means, and interval/ratio data allows for meaningful comparisons of the numerical values. Nominal or ordinal data cannot be used in ANOVA as they lack numerical values and do not allow for meaningful comparisons of the numerical values. Therefore, the dependent variable must be measured at an interval/ratio level.

Question 9

Your research hypothesis is "In the population, the average number of days unauthorized immigrants stay in the United States is less than 450." What type of hypothesis test should be used?
A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Accepted Answer

A one-sample t test is the appropriate choice for testing a hypothesis about a population mean when the sample size is small (n < 30) and the population standard deviation is unknown. This test is used to infer conclusions about a population from a sample and determine whether the sample provides strong evidence against a hypothesis about the population. The null hypothesis is that the average number of days unauthorized immigrants stay in the United States is equal to or greater than 450, and the alternative hypothesis is that the average is less than 450.

Question 10

"The educational attainment difference between persons raised by a single parent and persons raised by two parents is larger for lower social class families than for upper social class families." This is a description of
A) an interaction effect involving type of household in which raised and social class
B) a main effect of educational attainment
C) a main effect of social class
D) a main effect of type of household in which raised

Accepted Answer

The statement describes an interaction effect between the type of household in which a person was raised and their social class. The educational attainment difference between those raised in single-parent households versus those raised in two-parent households is larger for individuals from lower social class families compared to those from upper social class families.

Question 11

You want to know if two variables significantly interact in their effect on some variable. Which would be an appropriate procedure to use?
A) Frequencies
B) One-Way ANOVA
C) Paired-Samples T Test
D) Univariate General Linear Model (Two-Way ANOVA)

Accepted Answer

The Univariate General Linear Model (Two-Way ANOVA) is the appropriate procedure for examining if two variables significantly interact in their effect on some variable. This model is used when there are two independent variables and one dependent variable. It allows the researcher to test not only the main effects of each independent variable, but also their interaction effect on the dependent variable.

Question 12

Your research hypothesis is "In the population, there is a difference in the average self-confidence among the following groups: Protestants, Catholics, Jews, other religionists, and atheists." What type of hypothesis test should be used?
A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Accepted Answer

The hypothesis involves comparing the means of multiple groups, therefore a one-way ANOVA test would be appropriate.

Question 13

You want to know if there are any significant differences between the means of three groups, and, if so, between which groups. Which would be an appropriate procedure to use?
A) Frequencies
B) One Sample T Test
C) One-Way ANOVA
D) Paired-Samples T Test

Accepted Answer

One-Way ANOVA is the appropriate procedure to use when comparing the means of three or more groups. It determines if there is a significant difference between the means and, if so, which specific groups differ significantly from one another.

Question 14

You are doing a one-way ANOVA and the sample results are consistent with the research hypothesis. On the basis of the following output, your results _____ significant and you _____ proceed to discuss the post-hoc multiple comparisons.
ANOVA
EDUC
$\begin{array}{|l|r|r|r|r|r|}
\hline & {\begin{array}{c}
\text { Sum of } \
\text { Squares }
\end{array}} &{\mathrm{df}} & \text { Mean Square } & \mathrm{F} & \text { Sig. } \
\hline \text { Between Groups } & 203.047 & 2 & 101.523 & 9.209 & .000 \
\text { Within Groups } & 2348.171 & 213 & 11.024 & & \
\text { Total } & 2551.218 & 215 & & & \
\hline
\end{array}$
A) are … should
B) are … should not
C) are not … should
D) are not … should not

Accepted Answer

The results are significant because the Sig. (p-value) is .000, indicating the results are statistically significant. Therefore, you should proceed to discuss the post-hoc multiple comparisons to explore differences between groups.

Question 15

Why is one-way ANOVA better than repeated independent-sample t tests for comparing means for three or more groups?
A) one-way ANOVA allows for a nominal dependent variable
B) one-way ANOVA is more likely to find a significant difference
C) repeated independent-samples t tests increase the chance of a Type I error
D) repeated independent-samples t tests increase the chance of multicollinearity

Accepted Answer

One-way ANOVA is preferred over multiple independent-sample t tests for comparing three or more groups because conducting multiple t tests increases the overall chance of committing a Type I error, which is falsely rejecting the null hypothesis. ANOVA controls for this error rate across the comparisons.

Question 16

Your research hypothesis is "In the population, first stays in the U.S. by unauthorized immigrants are on average longer than second stays in the U.S. by these same immigrants." What type of hypothesis test should be used?
A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Accepted Answer

A paired-samples t test should be used because the same group of unauthorized immigrants will be measured twice (first stay and second stay in the U.S.).

Question 17

Your research hypothesis is "In the population, the effect of occupation on number of work days per year lost due to injury varies by sex." What type of hypothesis test should be used?
A) one-sample t test
B) paired-samples t test
C) independent-samples t test
D) one-way ANOVA
E) two-way ANOVA

Accepted Answer

The research hypothesis involves three variables - occupation, number of work days lost, and sex. This suggests a two-way ANOVA analysis would be appropriate as it allows for the investigation of the effect of both occupation and sex on the number of work days lost.

Question 18

On the basis of this output, which of the following is true?
Tests of Between-Subjects Effects
Dependent Variable:KIDSBEST
$\begin{array}{|l|r|r|r|r|r|}
\hline \text { Source } & \begin{array}{c}
\text { Type III Sum } \
\text { of Squares }
\end{array} & \text { df } & \text { Mean Square } & \text { F } & {\text { Sig. }} \
\hline \text { Corrected Model } & 4.238^{a} & 5 & .848 & 1.174 & .325 \
\text { Intercept } & 327.547 & 1 & 327.547 & 453.553 & .000 \
\text { MARRIED } & 3.631 & 2 & 1.816 & 2.514 & .085 \
\text { SEX } & .701 & 1 & .701 & .971 & .326 \
\text { MARRIED* SEX } & 1.790 & 2 & .895 & 1.239 & .293 \
\text { Error } & 96.050 & 133 & .722 & & \
\text { Total } & 879.000 & 139 & & & \
\text { Corrected Total } & 100.288 & 138 & & & \
\hline
\end{array}$
a. R Squared $= .042 ($ Adjusted R Squared $= .006 )$
A) The overall model is not significant.
B) The interaction effect is significant.
C) The main effect of MARRIED is significant.
D) The main effect of SEX is significant.

Accepted Answer

The overall model is not significant because the significance (Sig.) value for the Corrected Model is .325, which is greater than the conventional alpha level of .05, indicating that the model does not significantly predict the dependent variable.

Question 19

You are doing a one-way ANOVA. Your research hypothesis is that there is a difference in the mean knowledge about the Bible between Baptists, Catholics, and Methodists. What is your null hypothesis?
A) All three groups have different mean knowledge.
B) All three groups have the same mean knowledge.
C) At least two groups have the same mean knowledge.
D) Knowledge of the Bible and religious affiliation are related.

Accepted Answer

The null hypothesis for a one-way ANOVA is that there is no significant difference in the means of the groups being compared. In this case, the null hypothesis would be that there is no significant difference in the mean knowledge about the Bible between Baptists, Catholics, and Methodists, which can be symbolized as H0: μ1 = μ2 = μ3. Therefore, the correct choice is B.

Question 20

Your research hypothesis is that there is a difference between Protestants, Catholics, and Jews in average reported ideal number of children (KIDSBEST) for a family. Your sample results are consistent with the _____ and you should proceed to _____.
Descriptives
KIDSBEST
$\begin{array}{|l|r|r|r|r|}
\hline & & & & \
& {\mathrm{N}} & \text { Mean } & \text { Std. Deviation } & \text { Std. Error } \
\hline \text { 1 Protestant } & 147 & 2.71 & 1.034 & .085 \
\text { 2 Catholic } & 44 & 2.59 & .996 & .150 \
\text { 3 Jewish } & 20 & 2.45 & .887 & .198 \
\text { Total } & 211 & 2.66 & 1.012 & .070 \
\hline
\end{array}$
A) null hypothesis … Step 3 (check significance level)
B) null hypothesis … Step 4 (state conclusion)
C) research hypothesis … Step 3 (check significance level)
D) research hypothesis … Step 4 (state conclusion)

Accepted Answer

The sample results show differences in the means of the ideal number of children (KIDSBEST) among Protestants, Catholics, and Jews, which is consistent with the research hypothesis that there is a difference. The next step is to check the significance level to determine if the observed differences are statistically significant.

Quiz 14: Analysis of Variance

Your research hypothesis is "In the population, the average number of days female unauthorized immigrants stay in the U.S. is longer than the average number of days male unauthorized immigrants stay in the U.S." What type of hypothesis test should be used?

An author reports the following information about a one-way ANOVA: F = 0.95, df = 3 and 48, p = .231. Which of the following is true?

You are doing a one-way ANOVA. What level of measurement is required on the two variables you are using? (Circle the letter of the correct answer.)

If race and gender have a significant interaction effect on years of schooling,

Your research hypothesis is "In the population, there is a difference in the average number of work days per year lost due to injury among the following groups: secretaries, professors, police officers, and ministers." What type of hypothesis test should be used?

You are doing a two-way ANOVA. What level of measurement is required for the dependent variable?

Your research hypothesis is "In the population, the average number of days unauthorized immigrants stay in the United States is less than 450." What type of hypothesis test should be used?

"The educational attainment difference between persons raised by a single parent and persons raised by two parents is larger for lower social class families than for upper social class families." This is a description of

You want to know if two variables significantly interact in their effect on some variable. Which would be an appropriate procedure to use?

Your research hypothesis is "In the population, there is a difference in the average self-confidence among the following groups: Protestants, Catholics, Jews, other religionists, and atheists." What type of hypothesis test should be used?

You want to know if there are any significant differences between the means of three groups, and, if so, between which groups. Which would be an appropriate procedure to use?

Why is one-way ANOVA better than repeated independent-sample t tests for comparing means for three or more groups?

Your research hypothesis is "In the population, first stays in the U.S. by unauthorized immigrants are on average longer than second stays in the U.S. by these same immigrants." What type of hypothesis test should be used?

Your research hypothesis is "In the population, the effect of occupation on number of work days per year lost due to injury varies by sex." What type of hypothesis test should be used?

You are doing a one-way ANOVA. Your research hypothesis is that there is a difference in the mean knowledge about the Bible between Baptists, Catholics, and Methodists. What is your null hypothesis?