Question 1

A researcher reports the following result for a two-tailed test at a .05 level of significance,t(30)= 2.320,and correctly decides to retain the null hypothesis.

Accepted Answer

The critical value for a two-tailed t-test with 30 degrees of freedom at a .05 level of significance is +/- 2.042. Since the calculated t-value (2.320) exceeds the critical value, the result is statistically significant and the null hypothesis should be rejected. Therefore, the correct answer is B - the researcher should reject the null hypothesis, not retain it.

Question 2

When scores are measured in a single group,the sample standard deviation is used as an estimate of the population standard deviation in the effect size formula for estimated Cohen's d.

Accepted Answer

When only one group is being measured, the sample standard deviation is used as an estimate of the population standard deviation in the formula for Cohen's d.

Question 3

If d = 0.28,then we conclude that mean scores in some population have shifted 0.28 standard deviations below the mean.

Accepted Answer

The statement seems to refer to a value (d) that could be interpreted as a measure of effect size or difference, such as Cohen's d. However, Cohen's d specifically measures the difference between two means in terms of standard deviations, not a shift in the mean of a single population. Saying "mean scores in some population have shifted 0.28 standard deviations below the mean" misinterprets what such a statistic represents.

Question 4

A one-sample t test will be undefined (denominator = 0)when the same score is recorded for all participants in a study.

Accepted Answer

A one-sample t test compares the mean of a sample to a known population mean. If all scores in the sample are the same, there is no variation in the sample and the standard deviation is 0, causing the denominator of the t test formula to be 0, which would make the test undefined.

Question 5

The p value is reported with the test statistic of a one-sample and a two-independent sample t test using APA format.

Accepted Answer

The p value is an essential component of reporting the results of a one-sample or a two-independent sample t test in APA format. The p value indicates the probability of obtaining the observed results by chance, and it is reported along with the test statistic, degrees of freedom, and effect size measures (if applicable) in APA format.

Question 6

Measures of proportion of variance are computed the same for all t tests.

Accepted Answer

The answer of Measures of proportion of variance are computed...

Question 7

A two-independent sample t test is computed when mean differences are compared between two or more groups sampled from a population with an unknown variance.

Accepted Answer

A two-independent-sample t test is used for comparing mean differences between exactly two groups, not two or more groups, sampled from populations with unknown variances. For comparing means across more than two groups, an ANOVA is typically used.

Question 8

An estimated Cohen's d is interpreted in terms of the number of standard deviations that an effect shifted in some population.

Accepted Answer

An estimated Cohen's d represents the standardized difference between two means and is typically interpreted in terms of the number of standard deviations that an effect shifted in some population.

Question 9

A researcher reports that the mean difference between two groups is 20.12 and the estimated standard error for the difference is 2.83.Hence,the conclusion must be to reject the null hypothesis for a two-tailed test at a .05 level of significance.

Accepted Answer

The researcher has provided the mean difference between two groups and the estimated standard error for the difference, which allows us to calculate a t-statistic. If the calculated t-statistic exceeds the critical value at the chosen level of significance (in this case, .05), then we reject the null hypothesis. Without actually calculating the t-statistic or critical value, we can conclude that the given information suggests rejection of the null hypothesis since the mean difference is large and the estimated standard error is relatively small. Therefore, the correct answer is A) True.

Question 10

Eta-squared is a more conservative estimate than omega-squared.

Accepted Answer

Eta-squared is a biased estimate of effect size because it is dependent on the sample size. On the other hand, omega-squared is an unbiased estimate of effect size because it is not dependent on the sample size. Therefore, omega-squared is a more conservative estimate of effect size than eta-squared.

Question 11

When the difference between two groups is compared,the pooled standard deviation is used as an estimate for the population standard deviation in the effect size formula for estimated Cohen's d.

Accepted Answer

This is true. Pooled standard deviation is used as an estimate for the population standard deviation in effect size formula for estimated Cohen's d when the difference between two groups is compared.

Question 12

The critical values are reported with the test statistic of a one-sample and a two-independent sample t test using APA format.

Accepted Answer

The critical values are not typically reported in APA format for t tests. The p-value, degrees of freedom, and test statistic are typically reported.

Question 13

A researcher reports the following result for a lower-tail critical test at a .05 level of significance,t(40)= 3.212,and accurately concludes that this result is significant.

Accepted Answer

For a lower-tail test at a .05 significance level, the critical t-value would be negative. A positive t-value like 3.212 would not fall in the critical region for a lower-tail test, so the result is not significant.

Question 14

A two-independent sample t test is used when the same participants are observed in each of two groups.

Accepted Answer

A two-independent sample t test is used when two separate and distinct groups of participants are observed, rather than the same participants being observed in both groups. This allows for a comparison of means between the two groups to determine if there is a statistically significant difference.

Question 15

When the proportion of variance explained by some treatment is larger than 0.25,we conclude that there is a large effect in the population.

Accepted Answer

A proportion of variance explained of 0.25 or greater is generally considered to indicate a large effect size in the population.

Question 16

A researcher computes a two-independent sample t test and finds that the result is undefined (the denominator is equal to 0).This happens when there is no difference between the two groups .

Accepted Answer

The undefined result of a two-independent sample t test occurs when the denominator is equal to 0, but this does not necessarily mean that there is no difference between the two groups. Other possible explanations include sample size issues or measurement error.

Question 17

Cohen's d is a measure of proportion of variance.

Accepted Answer

Cohen's d is a measure of effect size used to indicate the standardized difference between two means.

Question 18

Effect size measures are an estimate of the size of an effect in a population.

Accepted Answer

Effect size measures provide an estimate of the magnitude of an effect in a population rather than just determining if there is a statistically significant difference.

Question 19

A one-sample t test will be t = 0 when the standard error was equal to 0.

Accepted Answer

This statement is false. A one-sample t test cannot have a standard error equal to 0 because the formula for calculating the standard error includes dividing by the square root of the sample size. If the sample size is greater than 1, the standard error cannot be 0. If the standard error were 0, the t statistic would be undefined, not equal to 0.

Question 20

A one-sample t test will be t = 0 when the mean difference is equal to 0.

Accepted Answer

This is because the formula for the t-statistic includes the term (sample mean - population mean)/standard error of the mean. If the sample mean is equal to the population mean, the numerator would be 0, making the t-statistic 0 as well.

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