Question 1

When testing a hypothesis with one or two groups selected from a population with an unknown variance,a t test is appropriate.

Accepted Answer

A t test is appropriate when we are testing a hypothesis about the mean of a population when the population variance is unknown and the sample size is small (less than 30). This is because the t distribution allows us to estimate the population variance using the sample variance, which is used to calculate the test statistic. Therefore, if we have one or two groups selected from a population with an unknown variance, a t test is appropriate.

Question 2

$\eta$² is computed ______ for the one-sample and the two-independent-sample t tests.

Accepted Answer

The string of numbers and letters provided is a standardized format for reporting the results of t-tests. It includes information about the type of test (one-sample or two-independent-sample), the test statistic (t-value), the degrees of freedom (df), and the p-value. This format is used consistently for both types of t-tests, so the computation is done similarly for both.

Question 3

As the degrees of freedom for a t test increase,the critical values for that test also increase.

Accepted Answer

As the degrees of freedom for a t test increase, the critical values for that test decrease. This is because as the sample size increases, the sample mean is more likely to be closer to the population mean, so a less extreme t statistic is needed to reject the null hypothesis.

Question 4

A researcher reports a significant mean difference in a given population.If she computes both $\eta$² and $\omega$² to measure the effect size,then which estimate will be most conservative?

Accepted Answer

F1F1F1S1F1F1F10² is the most conservative estimate of effect size as it uses the larger variance estimate in the denominator, which leads to a smaller effect size estimate. The choice does not depend on sample size or t-statistic value.

Question 5

A researcher reports that the mean difference in response time to an auditory versus a visual cue is 0.83 s,with a pooled sample variance equal to 2.45.What is the effect size for this test using estimated Cohen's d?

Accepted Answer

Cohen's d is calculated as the mean difference divided by the square root of the pooled variance. Here, d = 0.83 / sqrt(2.45) ≈ 0.53. According to Cohen's conventions, 0.2, 0.5, and 0.8 represent small, medium, and large effect sizes, respectively. Thus, 0.53 indicates a medium effect size.

Question 6

Which measure of effect size is most commonly reported with a t test?

Accepted Answer

Cohen's d is the most commonly reported measure of effect size with a t test because it provides information about the standardized difference between two means, making it easier to compare the magnitude of effects across studies.

Question 7

A researcher reports that the effectiveness of a new marketing campaign significantly increased sales compared with the previous campaign strategy,t(49)= 2.562,p < .05.Use $\eta$² to interpret the effect size for this result.

Accepted Answer

The correct interpretation of the effect size, represented by "F1F1F1S1uf068F1F1F10²," is that 12% of the variability in marketing effectiveness can be accounted for by the new marketing strategy. This is typically how effect size is understood in the context of statistical analysis, indicating the proportion of variance in the dependent variable that is predictable from the independent variable.

Question 8

Is a one-sample t test reported differently for one-tailed and two-tailed tests?

Accepted Answer

The values reported for a one-sample t test are the same for both one-tailed and two-tailed tests. The difference lies in the interpretation of the p-value and determining statistical significance, but the reported values such as the mean, standard deviation, and t-statistic will remain the same.

Question 9

Normality is the assumption that data in the population are normally distributed.

Accepted Answer

Normality assumption assumes that the data in the population follow a normal distribution.

Question 10

Normality,random sampling,and independence are all assumptions for the one-sample t test.

Accepted Answer

Normality, random sampling, and independence are all assumptions for the one-sample t test. Therefore, the statement is true.

Question 11

A t statistic estimates the standard error by using the sample variance to approximate the population variance.

Accepted Answer

The t statistic formula uses the sample standard deviation to estimate the population standard deviation, not the sample variance.

Question 12

A researcher reports that the mean difference in the body weight of rats following a pharmacological versus control treatment is 14 g,with a pooled sample variance equal to 256.What is the effect size for this test using estimated Cohen's d?

Accepted Answer

To calculate Cohen's d, we need to divide the mean difference by the square root of the pooled sample variance, which is the square root of 256 or 16. 
d = 14/16 
d = 0.875 
This indicates a large effect size according to Cohen's guidelines, which state that effect sizes of 0.2, 0.5, and 0.8 represent small, medium, and large effects, respectively. Therefore, the correct answer is C.

Question 13

A t distribution with infinite degrees of freedom is a z distribution.

Accepted Answer

When the degrees of freedom in a t distribution approach infinity, the t distribution becomes more and more similar to a standard normal distribution (z distribution). Therefore, when the degrees of freedom are infinite, a t distribution is essentially a z distribution.

Question 14

A t test is associated with N degrees of freedom.

Accepted Answer

A t-test is associated with N-1 degrees of freedom, where N is the sample size.

Question 15

Two researchers (A and B)compute a two-independent-sample t test.For both tests,the standard error is the same,but the mean difference between the groups is larger for Researcher A.Which test is more likely to result in a decision to reject the null hypothesis?

Accepted Answer

The larger mean difference between groups for Researcher A indicates stronger evidence for rejecting the null hypothesis, therefore making it more likely that their test will result in a decision to reject the null hypothesis.

Question 16

A t test is associated with n - 1 degrees of freedom.

Accepted Answer

This is true. The number of degrees of freedom in a t test is equal to the sample size minus one (n - 1).

Question 17

A researcher reports the following result for a two-tailed test at a .05 level of significance,t(20)= 2.010,and correctly decides to reject the null hypothesis.

Accepted Answer

The critical t-value for a two-tailed test with 20 degrees of freedom at a .05 significance level is approximately ±2.086. Since 2.010 is less than 2.086, the null hypothesis should not be rejected.

Question 18

A researcher reports that stress levels among nurses are higher compared to stress levels in the general population,t(20)= 2.086,p = .05 (d = .12).Was this a one-tailed or a two-tailed test?

Accepted Answer

In hypothesis testing, the p-value is compared with the significance level (usually set at α = 0.05) to determine whether to accept or reject the null hypothesis. In this example, the reported p-value is equal to .05, which means that the researcher used a significance level of .05. Since the null hypothesis would be rejected if the sample mean was significantly different (either greater or less) from the population mean, we can assume that it is a two-tailed test. Therefore, the correct answer is B.

Question 19

Which of the following summarizes a t test that was significant and associated with a large effect size?

Accepted Answer

A significant t test (p < .05) with a large effect size (d = .82) indicates that the difference between the groups being studied is unlikely due to chance and is a meaningful difference in the population. Choice D is the only option that meets both criteria.

Question 20

A researcher must know the population variance in order to compute a t test.

Accepted Answer

A t test can still be computed using sample variance instead of population variance.

Quiz 9: Testing Means: One-Sample and Two-Independent-Sample T Tests

When testing a hypothesis with one or two groups selected from a population with an unknown variance,a t test is appropriate.

$\eta$ ² is computed ______ for the one-sample and the two-independent-sample t tests.

As the degrees of freedom for a t test increase,the critical values for that test also increase.

A researcher reports a significant mean difference in a given population.If she computes both $\eta$ ² and $\omega$ ² to measure the effect size,then which estimate will be most conservative?

A researcher reports that the mean difference in response time to an auditory versus a visual cue is 0.83 s,with a pooled sample variance equal to 2.45.What is the effect size for this test using estimated Cohen's d?

Which measure of effect size is most commonly reported with a t test?

A researcher reports that the effectiveness of a new marketing campaign significantly increased sales compared with the previous campaign strategy,t(49) = 2.562,p < .05.Use $\eta$ ² to interpret the effect size for this result.

Is a one-sample t test reported differently for one-tailed and two-tailed tests?

Normality is the assumption that data in the population are normally distributed.

Normality,random sampling,and independence are all assumptions for the one-sample t test.

A t statistic estimates the standard error by using the sample variance to approximate the population variance.

A researcher reports that the mean difference in the body weight of rats following a pharmacological versus control treatment is 14 g,with a pooled sample variance equal to 256.What is the effect size for this test using estimated Cohen's d?

A t distribution with infinite degrees of freedom is a z distribution.

A t test is associated with N degrees of freedom.

Two researchers (A and B) compute a two-independent-sample t test.For both tests,the standard error is the same,but the mean difference between the groups is larger for Researcher A.Which test is more likely to result in a decision to reject the null hypothesis?

A t test is associated with n - 1 degrees of freedom.

A researcher reports the following result for a two-tailed test at a .05 level of significance,t(20)= 2.010,and correctly decides to reject the null hypothesis.

A researcher reports that stress levels among nurses are higher compared to stress levels in the general population,t(20) = 2.086,p = .05 (d = .12) .Was this a one-tailed or a two-tailed test?

Which of the following summarizes a t test that was significant and associated with a large effect size?

A researcher must know the population variance in order to compute a t test.

Quiz 9: Testing Means: One-Sample and Two-Independent-Sample T Tests

When testing a hypothesis with one or two groups selected from a population with an unknown variance,a t test is appropriate.

η\etaη 2 is computed ______ for the one-sample and the two-independent-sample t tests.

As the degrees of freedom for a t test increase,the critical values for that test also increase.

A researcher reports a significant mean difference in a given population.If she computes both η\etaη 2 and ω\omegaω 2 to measure the effect size,then which estimate will be most conservative?

A researcher reports that the mean difference in response time to an auditory versus a visual cue is 0.83 s,with a pooled sample variance equal to 2.45.What is the effect size for this test using estimated Cohen's d?

Which measure of effect size is most commonly reported with a t test?

A researcher reports that the effectiveness of a new marketing campaign significantly increased sales compared with the previous campaign strategy,t(49) = 2.562,p < .05.Use η\etaη 2 to interpret the effect size for this result.

Is a one-sample t test reported differently for one-tailed and two-tailed tests?

Normality is the assumption that data in the population are normally distributed.

Normality,random sampling,and independence are all assumptions for the one-sample t test.

A t statistic estimates the standard error by using the sample variance to approximate the population variance.

A researcher reports that the mean difference in the body weight of rats following a pharmacological versus control treatment is 14 g,with a pooled sample variance equal to 256.What is the effect size for this test using estimated Cohen's d?

A t distribution with infinite degrees of freedom is a z distribution.

A t test is associated with N degrees of freedom.

Two researchers (A and B) compute a two-independent-sample t test.For both tests,the standard error is the same,but the mean difference between the groups is larger for Researcher A.Which test is more likely to result in a decision to reject the null hypothesis?

A t test is associated with n - 1 degrees of freedom.

A researcher reports the following result for a two-tailed test at a .05 level of significance,t(20)= 2.010,and correctly decides to reject the null hypothesis.

A researcher reports that stress levels among nurses are higher compared to stress levels in the general population,t(20) = 2.086,p = .05 (d = .12) .Was this a one-tailed or a two-tailed test?

Which of the following summarizes a t test that was significant and associated with a large effect size?

A researcher must know the population variance in order to compute a t test.

$\eta$ ² is computed ______ for the one-sample and the two-independent-sample t tests.

A researcher reports a significant mean difference in a given population.If she computes both $\eta$ ² and $\omega$ ² to measure the effect size,then which estimate will be most conservative?

A researcher reports that the effectiveness of a new marketing campaign significantly increased sales compared with the previous campaign strategy,t(49) = 2.562,p < .05.Use $\eta$ ² to interpret the effect size for this result.