Question 1

An agricultural experiment will be done to compare the effectiveness of two different soil treatments. Which of the following sample sizes would lead to a test with the lowest power?

Accepted Answer

A smaller sample size generally leads to a test with lower power because it is less likely to detect a true effect if one exists.

Question 2

An experiment will be conducted to compare the effectiveness of a new treatment against a placebo. Which of the following combinations would lead to a test with the highest power?

Accepted Answer

The power of a test increases with larger sample sizes and larger differences between the means of the groups being compared. Option D has the largest sample sizes and the largest difference between means, leading to the highest power.

Question 3

A study compared the average number of courses taken by a random sample of freshmen at a university with the average number of courses taken by a separate random sample of freshmen at a community college. Which of the following combinations would lead to a test with the highest power?

Accepted Answer

The power of a test increases with larger sample sizes and larger differences between the means. Option B has the largest sample sizes and maintains the larger mean difference of 1.2, leading to the highest power.

Question 4

When the alternative hypothesis is true, which one of these statements about the power of a significance test is correct?

Accepted Answer

The power of a test is indeed the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true, which is equivalent to not making a Type 2 error.

Question 5

If the word significant is used to describe a result in a news article reporting on a study,

Accepted Answer

The term "significant" in a news article may not always refer to statistical significance, which is related to p-values in hypothesis testing, but could be used in its everyday sense to mean "important" or "noteworthy." The other options incorrectly describe statistical concepts related to significance.

Question 6

Use the following information for questions:
 Cholesterol measurements for a sample of males following a new diet plan gave a mean of 208 and a standard deviation of 10.
-What is the estimated effect size for comparing this result to the 200 level?

Accepted Answer

The effect size is calculated as the difference between the mean and the comparison value, divided by the standard deviation. Here, it is (208 - 200) / 10 = 8 / 10 = 0.8.

Question 7

Use the following information for questions:
 Cholesterol measurements for a sample of males following a new diet plan gave a mean of 208 and a standard deviation of 10.
-Based on Cohen's interpretation, this effect is

Accepted Answer

The answer of Use the following information for questions:
 Cholesterol...

Question 8

Use the following information for questions:
 A sample of passengers flying on small planes gave a mean total weight (passenger weight including shoes, clothes, and carry-on) of 200 pounds and a standard deviation of 60 pounds.
-What is the estimated effect size for comparing this result to the FDA guideline level of 185 pounds?

Accepted Answer

The effect size is calculated as the difference between the mean and the guideline level divided by the standard deviation: (200 - 185) / 60 = 15 / 60 = 0.25.

Question 9

Use the following information for questions:
 A sample of passengers flying on small planes gave a mean total weight (passenger weight including shoes, clothes, and carry-on) of 200 pounds and a standard deviation of 60 pounds.
-Based on Cohen's interpretation, this effect is

Accepted Answer

The effect size is calculated as the mean difference divided by the standard deviation. In this case, the effect size is 200/60 = 3.33. According to Cohen's interpretation, an effect size of 0.2 is considered small, an effect size of 0.5 is considered medium, and an effect size of 0.8 is considered large. Therefore, the effect size of 3.33 is considered large, which means that the effect is obvious to most observers.

Question 10

Use the following information for questions:
 A pooled two independent samples t-test was conducted to compare the average number of accidents for male drivers to that for female drivers. The t-test statistic was 2.4 and the sample sizes were 32 males and 30 females.
-What is the estimated effect size for this study?

Accepted Answer

The estimated effect size for a t-test can be calculated using Cohen's d, which is the difference between two means divided by the pooled standard deviation. The t-test statistic itself does not directly give the effect size, but it can be used in conjunction with sample sizes to estimate Cohen's d. The correct answer is not directly calculable from the information given without the means or standard deviations, but among the options provided, 0.61 is a plausible value for Cohen's d, indicating a moderate effect size, while the other options do not represent typical effect size values.

Question 11

Use the following information for questions:
 A pooled two independent samples t-test was conducted to compare the average number of accidents for male drivers to that for female drivers. The t-test statistic was 2.4 and the sample sizes were 32 males and 30 females.
-Based on Cohen's interpretation, this effect is

Accepted Answer

A t-test statistic of 2.4 typically indicates a medium effect size, which is noticeable to careful observers according to Cohen's interpretation.

Question 12

What is the estimated effect size for a test for the difference between two population means with independent samples with sizes of 25 and 35 respectively and a pooled t-test statistic of t = -2.34?

Accepted Answer

The effect size (Cohen's d) can be estimated using the formula: d = t * sqrt((1/n1) + (1/n2)), where n1 and n2 are the sample sizes. Substituting the given values: d = -2.34 * sqrt((1/25) + (1/35)) ≈ -0.61.

Question 13

Compute the effect size in a one-sample t-test with a sample size of n = 66 and a test statistic of t = 2.27. How is the effect size interpreted based on Cohen's guidelines?

Accepted Answer

The effect size (Cohen's d) in a one-sample t-test can be calculated as $d = \frac{t}{\sqrt{n}}$, where $t$ is the test statistic and $n$ is the sample size. Plugging in the given values, $d = \frac{2.27}{\sqrt{66}} \approx 0.28$. According to Cohen's guidelines, an effect size of 0.2 is considered small, 0.5 medium, and 0.8 large, making 0.28 a small effect.

Question 14

A random sample of 25 third graders scored an average of 3.4 on a standardized reading test. The standard deviation was 0.95. A test is conducted to determine if the mean score is significantly higher than 3. What is the effect size of this test?

Accepted Answer

The effect size can be calculated using Cohen's d, which is the difference between the mean score and the hypothesized mean, divided by the standard deviation: $d = \frac{\bar{x} - \mu}{s} = \frac{3.4 - 3}{0.95} = \frac{0.4}{0.95} = 0.42$.

Question 15

Use the following information for questions:
A group of women suffering from various types of obsessive fear is given a therapeutic course to learn how to handle their fear. At the end of the course the women are given a questionnaire to determine how afraid they are. Six months after the course the women answer the questionnaire again as a follow-up measure. The fear-scores are typed into SPSS. Output of the paired samples t-test is shown below. 
-What is the effect size that should be reported with this test?

Accepted Answer

The answer of Use the following information for questions:
A group...

Question 16

Use the following information for questions:
A group of women suffering from various types of obsessive fear is given a therapeutic course to learn how to handle their fear. At the end of the course the women are given a questionnaire to determine how afraid they are. Six months after the course the women answer the questionnaire again as a follow-up measure. The fear-scores are typed into SPSS. Output of the paired samples t-test is shown below. 
-Based on Cohen's interpretation, this effect is

Accepted Answer

The answer of Use the following information for questions:
A group...

Question 17

Explain what the effect size measures.

Accepted Answer

The answer of Explain what the effect size measures....

Question 18

Explain the role of effect size in meta-analyses.

Accepted Answer

The answer of Explain the role of effect size in...

Question 19

Using Cohen's interpretation of effect size, what would an effect size of d = 0.12 be interpreted as?

Accepted Answer

The answer of Using Cohen's interpretation of effect size, what...

Question 20

Using Cohen's interpretation of effect size, what would an effect size of d = −0.52 be interpreted as?

Accepted Answer