Question 1

For which of the following hypotheses is a one-tailed test of significance appropriate?
A) Teaching method A and teaching method B will produce different student achievement gains.
B) There is no difference in the effects of Head Start programs on the achievement gains of low-income Caucasian and African-American children.
C) The mean IQ score of a sample is significantly different from the population mean.
D) Children receiving a dietary supplement will show greater achievement gains than those receiving a placebo.

Accepted Answer

A one-tailed test of significance is appropriate when the hypothesis predicts a direction of the effect, such as expecting one group to score higher or lower than another. Option D predicts that children receiving a dietary supplement will show greater achievement gains than those receiving a placebo, indicating a specific direction and thus making a one-tailed test appropriate. Options A, B, and C suggest comparisons without specifying a direction of difference or are testing for any significant difference, which would require a two-tailed test.

Question 2

Use of a one-tailed versus a two-tailed t test to test the significance of the difference between two sample means depends on whether
A) there is expected overlap between the error curves of the two sample distributions.
B) the difference is expected to be in one direction only.
C) the size of the samples is proportional to their respective population sizes.
D) research participants were matched or chosen randomly.

Accepted Answer

A one-tailed t-test is used when the difference is expected to be in one direction only, allowing for testing a specific hypothesis about the direction of the difference between two sample means.

Question 3

If any of the assumptions underlying the t test are violated to a modest extent,
A) the t test is still likely to yield an accurate estimate of statistical significance.
B) the t test will yield an accurate estimate of statistical significance, but only if the test is two-tailed.
C) a nonparametric test of statistical significance must be used instead.
D) no test of statistical significance should be performed.

Accepted Answer

The t test is robust to modest violations of its assumptions, meaning it can still provide accurate estimates of statistical significance even if the assumptions are not perfectly met. This robustness is particularly true for violations of normality when sample sizes are large enough.

Question 4

The t test for correlated means should be used when
A) the group possessing the characteristic of interest and the comparison group are randomly selected.
B) subgroups are to be formed within the group possessing the characteristic of interest.
C) the group possessing the characteristic of interest and the comparison group are matched on another variable.
D) researchers wish to determine the magnitude of the relationship between independent and dependent variables.

Accepted Answer

The t-test for correlated means is appropriate when the two groups being compared are matched or paired on some variable, ensuring that the comparison between the groups takes into account the matching variable, which is meant to control for its effects.

Question 5

In comparing the mean performance of 25 delinquents and 25 matched nondelinquents, one should use the
A) t test for independent means.
B) z distribution.
C) t test for a single mean.
D) t test for correlated means.

Accepted Answer

The answer of In comparing the mean performance of 25...

Question 6

Match each condition below with the test most appropriate under that condition To determine whether:
-the sample mean differs significantly from a specified population mean.
A) t test for correlated means
B) t test for a single mean
C) chi-square test
D) analysis of variance
E) t test for independent means

Accepted Answer

The t test for a single mean is specifically designed to compare the mean of a single sample to a known population mean to determine if there is a significant difference.

Question 7

Match each condition below with the test most appropriate under that condition To determine whether:
-the mean achievement of a random sample of delinquents differs significantly from that of a randomly selected control group.
A) t test for correlated means
B) t test for a single mean
C) chi-square test
D) analysis of variance
E) t test for independent means

Accepted Answer

The t test for independent means is used when comparing the means of two independent groups to see if there is a significant difference between them. In this scenario, the groups are delinquents and a control group, which are independent of each other.

Question 8

Match each condition below with the test most appropriate under that condition To determine whether:
-the mean anxiety scores of high, middle, and low achievers are significantly different.
A) t test for correlated means
B) t test for a single mean
C) chi-square test
D) analysis of variance
E) t test for independent means

Accepted Answer

The analysis of variance (ANOVA) is the appropriate test when comparing the means of more than two groups to determine if there is a significant difference among them. In this case, comparing the mean anxiety scores of high, middle, and low achievers involves three groups, making ANOVA the correct choice.

Question 9

Match each condition below with the test most appropriate under that condition To determine whether:
-high, middle, and low achievers have different high school dropout rates.
A) t test for correlated means
B) t test for a single mean
C) chi-square test
D) analysis of variance
E) t test for independent means

Accepted Answer

The chi-square test is appropriate for comparing categorical data, such as dropout rates, across different groups (high, middle, and low achievers).

Question 10

Match each condition below with the test most appropriate under that condition To determine whether:
-the mean achievement of two groups of students matched on aptitude differs significantly.
A) t test for correlated means
B) t test for a single mean
C) chi-square test
D) analysis of variance
E) t test for independent means

Accepted Answer

The t test for correlated means is appropriate for comparing the means of two related groups, such as groups of students who are matched on a variable like aptitude. This test accounts for the fact that the groups are not independent of each other.

Question 11

Use of the t test for a single mean requires
A) a normal score distribution.
B) homogeneity of variance.
C) random selection of research participants.
D) knowledge of the population mean.

Accepted Answer

The answer of Use of the t test for a...

Question 12

If a researcher wishes to determine whether a sample mean differs from the population mean, the appropriate statistic is the
A) chi-square.
B) t test for independent means.
C) t test for a single mean.
D) analysis of covariance.

Accepted Answer

The t test for a single mean is specifically designed to compare a sample mean to a known population mean to determine if there is a significant difference between them. This test assesses whether the observed sample mean is statistically significantly different from the hypothesized population mean, based on the sample's standard deviation and size.

Question 13

The F ratio is computed to determine
A) whether the members of a sample have been randomly selected from a population.
B) the statistical significance of the difference between the mean scores of two or more groups.
C) whether two or more groups have different frequency distributions on a categorical variable.
D) all of the above.

Accepted Answer

The F ratio is used in analysis of variance (ANOVA) to determine the statistical significance of the difference between the mean scores of two or more groups. It compares the variance between groups to the variance within groups to assess if the group means differ more than would be expected by chance.

Question 14

Analysis of variance focuses on the
A) between-groups variance.
B) within-groups variance.
C) ratio of between-groups variance to within-groups variance.
D) mean scores of each group in the analysis.

Accepted Answer

Analysis of variance (ANOVA) primarily focuses on the ratio of between-groups variance to within-groups variance. This ratio helps in determining whether there are any statistically significant differences between the means of three or more independent (unrelated) groups.

Question 15

The purpose of the t test for multiple comparisons is to
A) adjust for statistically significant differences that occur by chance because the comparison groups are compared on many variables.
B) provide an alternative approach to multiple comparisons when the assumptions underlying analysis of variance are not satisfied.
C) enable the use of analysis of variance when the number of comparison groups exceeds five.
D) all of the above.

Accepted Answer

The t test for multiple comparisons is designed to adjust for statistically significant differences that might occur by chance when multiple groups are compared across various variables. This adjustment helps to ensure that observed differences are more likely to reflect true differences rather than random variation.

Question 16

Analysis of covariance is the preferred test rather than analysis of variance when
A) there are initial differences between the samples on a measured variable related to the dependent variable.
B) there are extreme differences in the sample variances.
C) the scores of the groups being compared are in the form of categorical frequency counts.
D) the scores of the groups being compared are in the form of ranks.

Accepted Answer

Analysis of covariance (ANCOVA) is used over analysis of variance (ANOVA) when there are pre-existing differences between the groups on a covariate that is related to the dependent variable. ANCOVA can adjust for these differences, making the groups more comparable.

Question 17

In conducting a MANOVA on a cluster of five related variables, a researcher obtains an F value that is significant at the .01 level. What is the next step that should be taken in analyzing the data?
A) Reexamine the cluster to see if any variables should be removed.
B) Test for the equality of group dispersions.
C) Compute a mean vector score for each variable.
D) Conduct an ANOVA on each dependent variable in the cluster.

Accepted Answer

When a MANOVA (Multivariate Analysis of Variance) yields a significant F value, indicating that there are overall differences among the groups on the combined dependent variables, the next step is often to conduct separate ANOVAs (Analysis of Variance) on each dependent variable. This helps to identify which specific variables are contributing to the significant multivariate effect observed in the MANOVA.

Question 18

The test for homogeneity of independent variances, the test for homogeneity of related variances, and theF maximum test for homogeneity of variance are all forms of
A) analysis of covariance.
B) nonparametric statistics.
C) analysis of variance.
D) multivariate analysis of variance.

Accepted Answer

These tests are all related to the analysis of variance (ANOVA), which is used to determine if there are any statistically significant differences between the means of three or more independent (unrelated) groups.

Question 19

Compared to parametric statistics, nonparametric statistics
A) have less statistical power.
B) have more statistical power.
C) involve many more assumptions about score distribution in the population being studied.
D) cannot be used to determine whether a null hypothesis can be rejected.

Accepted Answer

Nonparametric statistics typically have less statistical power compared to parametric statistics because they do not assume a specific distribution for the data, which often leads to less precise estimates.

Question 20

Chi-square should be used when data are in the form of
A) ranks.
B) standard scores.
C) continuous scores.
D) category frequencies.

Accepted Answer

Chi-square tests are used for data in the form of category frequencies, where the observations are categorized into a finite number of categories and the analysis is based on the counts or frequencies within those categories.

Quiz 10: Nonexperimental Research Descriptive and Causal-Comparative Designs

For which of the following hypotheses is a one-tailed test of significance appropriate?

Use of a one-tailed versus a two-tailed t test to test the significance of the difference between two sample means depends on whether

If any of the assumptions underlying the t test are violated to a modest extent,

The t test for correlated means should be used when

In comparing the mean performance of 25 delinquents and 25 matched nondelinquents, one should use the

Match each condition below with the test most appropriate under that condition To determine whether: -the sample mean differs significantly from a specified population mean.

Match each condition below with the test most appropriate under that condition To determine whether: -the mean achievement of a random sample of delinquents differs significantly from that of a randomly selected control group.

Match each condition below with the test most appropriate under that condition To determine whether: -the mean anxiety scores of high, middle, and low achievers are significantly different.

Match each condition below with the test most appropriate under that condition To determine whether: -high, middle, and low achievers have different high school dropout rates.

Match each condition below with the test most appropriate under that condition To determine whether: -the mean achievement of two groups of students matched on aptitude differs significantly.

Use of the t test for a single mean requires

If a researcher wishes to determine whether a sample mean differs from the population mean, the appropriate statistic is the

The F ratio is computed to determine

Analysis of variance focuses on the

The purpose of the t test for multiple comparisons is to

Analysis of covariance is the preferred test rather than analysis of variance when

In conducting a MANOVA on a cluster of five related variables, a researcher obtains an F value that is significant at the .01 level. What is the next step that should be taken in analyzing the data?

The test for homogeneity of independent variances, the test for homogeneity of related variances, and theF maximum test for homogeneity of variance are all forms of

Compared to parametric statistics, nonparametric statistics

Chi-square should be used when data are in the form of