Stats Quiz 11/13/24

Which of the following best describes the purpose of calculating a difference score in research?

• To determine the absolute value of scores at two different times.

• To assess whether there is a meaningful change in a single variable over time or between related pairs.

• To compare the average scores of two unrelated groups.

• To measure the variability of scores within a single sample.

Tags

CCSS.7.SP.B.3

A researcher conducts a study to determine if a training program leads to improved test scores. They calculate the average difference score between pre- and post-training scores and find it is significantly greater than zero. What conclusion can they draw based on this result?

• The null hypothesis is supported, indicating no change occurred.

• The null hypothesis is rejected, suggesting the training program was effective in improving scores.

• The alternative hypothesis is rejected, indicating the training program had no effect.

• The difference scores cannot be interpreted without knowing the raw pre- and post-training scores.

Tags

CCSS.HSS.IC.B.4

A researcher calculates a test statistic for a related-samples t-test. Which of the following best describes how the test statistic is determined?

• By comparing the raw scores at Time 1 and Time 2.

• By dividing the mean difference score by the standard error of the difference scores.

• By summing all the difference scores and dividing by the population size.

• By calculating the standard deviation of the raw scores and dividing it by the sample size.

What role does the critical value play in the decision-making process of a related-samples t-test?

• It determines the mean of the difference scores.

• It establishes the standard deviation of the sample.

• It serves as the threshold for deciding whether to reject the null hypothesis.

• It indicates the effect size of the observed difference.

Tags

CCSS.HSS.ID.A.4

In the context of a related-samples t-test, why is the null hypothesis value always set to 0?

• Because it assumes no difference or change occurred in the sample.

• Because the test statistic cannot be calculated otherwise.

• Because raw scores from Time 1 and Time 2 are expected to be identical.

• Because the standard error is only valid when the null hypothesis is 0.

A company implements a new policy and measures employee satisfaction before and after the intervention. The difference scores are analyzed using a related-samples t-test. What does a statistically significant result indicate?

• The intervention had no measurable impact on employee satisfaction.

• The intervention caused a statistically significant change in satisfaction levels.

• The employees' satisfaction scores were inconsistent across time points.

• The satisfaction levels did not deviate significantly from their initial values.

If a researcher calculates an effect size (Cohen’s d) for a related-samples t-test, what does a large value (e.g., d = 1.04) suggest about the intervention being studied?

• A. The intervention had a negligible impact on the outcome variable.

• B. The intervention had a small but statistically significant effect.

• C. The intervention had a strong and meaningful impact on the outcome variable.

• D. The intervention effect was likely due to random chance.

A bank conducts a two-tailed hypothesis test to evaluate changes in public opinion after showing a new commercial. The confidence interval for the difference scores is calculated as (-1.86, 3.00), which includes 0. How should the bank interpret this result?

• A. The commercial caused a significant positive change in public opinion.

• B. The commercial caused a significant negative change in public opinion.

• C. The change in public opinion is not statistically significant, as 0 is within the confidence interval.

• D. The commercial had no impact, and the opinions were identical before and after viewing.

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CCSS.HSS.IC.B.4

Why is the inclusion of 0 in the confidence interval critical for evaluating the null hypothesis in this scenario?

• It demonstrates the confidence interval was calculated correctly. 

• It confirms that the null hypothesis cannot be rejected because 0 represents no change. 

• It proves that the sample size was too small to calculate meaningful results.

• It implies the difference scores are too small to matter practically. 

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CCSS.HSS.IC.B.4

It demonstrates the confidence interval was calculated correctly. What does this imply?

• A. It demonstrates the confidence interval was calculated correctly.

• B. It confirms that the null hypothesis cannot be rejected because 0 represents no change.

• C. It proves that the sample size was too small to calculate meaningful results.

• D. It implies the difference scores are too small to matter practically.