2025 AP Statistics Free-Response Questions
Advanced PlacementFree ResponseMathematics
6 questions28.5 pts
6 gradable38 rubric criteria0 dependencies
q1
Question 1
1. The manager of an automotive company is interested in comparing the gas mileages for cars manufactured in Country A and cars manufactured in Country B. The manager selected a random sample of 100 cars manufactured in Country A and a random sample of 100 cars manufactured in Country B. The gas mileages for each sample, in miles per gallon (mpg), are summarized in the boxplots. Boxplots of Gas Mileage for Each Country A. Compare the distributions of gas mileage for the sample of cars manufactured in Country A and the sample of cars manufactured in Country B. B. For the distribution of gas mileage for the sample of cars manufactured in Country A, would you expect the mean to be greater than 18 mpg, less than 18 mpg, or equal to 18 mpg? Justify your answer. C. The manager will create a new boxplot with the combined data from the sample of cars manufactured in Country A and the sample of cars manufactured in Country B. i. What is the range of the combined data set? Justify your answer. ii. What is a possible value of the median of the combined data set? Justify your answer by referencing the boxplots shown.
Rubric Criteria (6)
A_EThe response satisfies at least three of the following four components for part A: (1) a direct comparison of the center for the two distributions (a response that relies only on means does not satisfy this component), (2) a direct comparison of the spread for the two distributions using either IQR or range (listing values without direct comparison is insufficient), (3) an indication that the gas mileage of one of the cars manufactured in Country A is an outlier, and (4) sufficient context including the manufacturing countries ("Country A" and "Country B") and the dependent variable ("gas mileage" or "mpg"). Acceptable mentions of shape are ignored; describing a shape as just "symmetric," "normal," "unimodal," or an incorrect shape prevents part A from being scored essentially correct.
1.0000pts
A_PThe response satisfies only two of the four components required for an essentially correct part A.
0.5000pts
B_EThe response satisfies all three of the following components for part B: (1) indicates that the mean of the distribution of gas mileage for the sample of cars manufactured in Country A is expected to be greater than 18 mpg, (2) indicates that 18 mpg is the value of the median (satisfied if stated in part A or B), and (3) provides a reasonable justification for the relationship between the mean and the median based on a right-skewed distribution or the expectation that an outlier in the right tail will pull the mean above the median (a weak justification such as "because the distribution is skewed" is insufficient; component 3 may also be satisfied with an appropriate numerical argument showing the mean must be greater than 18).
1.0000pts
B_PThe response satisfies component 1 (mean expected to be greater than 18 mpg) and either component 2 (indicates 18 as the median) or component 3 (reasonable justification) for part B.
0.5000pts
C_EThe response satisfies all four of the following components for part C: (1) correctly calculates 26 mpg as the range of the combined data set (values of 25 or 27 from misinterpreting the minimum as 13 or 15 may be considered a minor error and satisfy components 1 and 2), (2) provides a justification for the range by identifying 40 mpg as the maximum of the combined data set and 14 mpg as the minimum, (3) calculates 24 mpg as a possible value of the median of the combined data set, and (4) provides a justification for the median by indicating that at least half of the combined data values are at most 24 mpg and at least half are at least 24 mpg (justification may also be satisfied by examining quartiles on one side of 24 or by counting boxplot segments).
1.0000pts
C_PThe response satisfies only two or three of the four components required for an essentially correct part C.
0.5000pts
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q2
Question 2
2. Aphids are tiny insects that feed on plants such as cabbage plants. A farmer wants to reduce the number of aphids in a cabbage field. A river is located 100 meters south of the cabbage field. The farmer divides the field into 25 regions of equal size, as shown in the diagram. Each region has approximately the same number of cabbage plants. Farmer's House and Cabbage Field [Diagram: 5×5 grid with rows A–E and columns 1–5, containing regions numbered 1–25. The farmer's house is above row A. The river is 100 meters below row E.] The farmer would like to estimate the proportion of cabbage plants in the field that are affected by aphids and believes that the extent of aphid damage is greater for the regions in the cabbage field closer to the river. To obtain the estimate, the farmer is considering three sampling methods. • Sampling method I: Select region 3, which is closest to the farmer's house and farthest from the river. Examine every cabbage plant in the region for aphid damage. • Sampling method II: Randomly select one row (A, B, C, D, or E). For every region in the selected row, examine every cabbage plant for aphid damage. • Sampling method III: Randomly select one region from each of rows A, B, C, D, and E. For each selected region, examine every cabbage plant for aphid damage. A. Explain whether sampling method I is an appropriate sampling method for the farmer to use to estimate the proportion of cabbage plants in the field that are damaged by aphids. B. Using sampling method II, the farmer randomly selected row E and examined every cabbage plant in row E. If the farmer's belief is correct, determine whether the selection of row E is likely to provide an overestimate or an underestimate of the proportion of cabbage plants in the field that are damaged by aphids. Justify your answer. C. Using the information provided in the diagram of the cabbage field, describe how to implement sampling method III, which requires a random selection of one region from each of rows A, B, C, D, and E.
Rubric Criteria (6)
A_EThe response satisfies all three of the following components for part A: (1) indicates that sampling method I is not an appropriate sampling method to obtain the estimate, (2) provides an explanation referring to at least one of the following: the region is likely not representative of the entire cabbage field, the sampling process does not include random selection, or the sample is a convenience sample, and (3) provides sufficient context by including any two of the following: the sampling unit (region), the population (cabbage field or the 25 regions in the field), or the statistic or parameter (proportion of cabbage plants that are damaged by aphids) or count (number of cabbage plants that are damaged by aphids).
1.0000pts
A_PThe response satisfies component 1 (sampling method I is not appropriate) and either component 2 (explanation) or component 3 (context) for part A; OR the response does not indicate whether sampling method I is appropriate and satisfies both components 2 and 3.
0.5000pts
B_EThe response satisfies all three of the following components for part B: (1) indicates that the selection of row E is likely to produce an overestimate of the proportion of all cabbage plants in the field that are damaged by aphids, (2) provides a justification based on the location of row E as the row located closest to the river, and (3) links the location to why row E is likely to produce an overestimate by referring to the farmer's belief that the extent of aphid damage is greater for the regions in the cabbage field closer to the river.
1.0000pts
B_PThe response satisfies only two of the three components required for an essentially correct part B. (A response indicating an underestimate may be scored partially correct if it ignores the farmer's belief but includes a valid reason why regions further from the river may have more aphid damage.)
0.5000pts
C_EThe response satisfies all four of the following components for part C: (1) describes a random selection process that indicates the groupings used for the strata (by rows or the five regions in each row), (2) describes how to correctly implement a random selection process for which the selection of regions within each stratum is equally likely (e.g., same-size slips of paper in a hat mixed thoroughly; random number generator within each row with clearly equal likelihood; thorough mixing/shuffling is required for slips of paper), (3) describes a random selection process for which the selections across strata are independent (selecting columns instead of regions within strata does not satisfy this component), and (4) describes a random selection process that results in the selection of one region from each stratum. If two separate random selection processes are described in detail, score both and use the lower score.
1.0000pts
C_PThe response satisfies only two or three of the four components required for an essentially correct part C.
0.5000pts
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q3
Question 3
3. Ms. Fey is a manager at a restaurant. To improve the dining experience for her customers, she uses a digital music service to create a playlist of songs that will be played in the restaurant. The playlist contains 1,000 songs and consists of four different types of music in the following quantities: 200 country songs, 400 pop songs, 100 rock songs, and 300 jazz songs. The digital music service will select songs at random from the playlist to be played in the restaurant. Any song can be replayed at any time. A. i. Suppose one song is selected at random to be played. What is the probability that the song is a rock song? Show your work. ii. Suppose two songs are selected at random to be played. What is the probability that both songs are rock songs? Show your work. B. In every one-hour period, 20 songs will be played at random and any song can be replayed at any time. Ms. Fey is interested in how many rock songs will be played in a typical one-hour period. i. Define the random variable of interest to Ms. Fey, and state how the random variable is distributed. ii. What is the expected value for the random variable in part B (i)? Show your work. C. Recall that in every one-hour period, 20 songs will be played at random and any song can be replayed at any time. i. Determine the probability that 4 or more rock songs in a particular one-hour period will be played. Show your work. ii. Suppose 4 rock songs are played during a particular one-hour period. Does this provide strong evidence that the song selection process was not truly random? Justify your answer without performing an inference procedure.
Rubric Criteria (6)
A_EThe response satisfies all four of the following components for part A: (1) in part (i) calculates the correct probability of selecting a rock song as 0.10 (or equivalent fraction/percent) with supporting work, (2) in part (i) provides supporting work for the correct probability, (3) in part (ii) calculates the correct probability of both songs being rock songs as 0.01 (or consistent with the answer in part (i)) with supporting work, and (4) in part (ii) provides supporting work consistent with the probability calculated in part (i) (a response using 99/999 without considering independence satisfies component 4 but not component 3).
1.0000pts
A_PThe response satisfies two or three of the four components required for an essentially correct part A.
0.5000pts
B_EThe response satisfies at least three of the following four components for part B: (1) defines the random variable as the number of rock songs played in one hour (or out of 20 songs), (2) describes the distribution as binomial (stating songs are distributed randomly is extraneous; stating another distribution prevents scoring E), (3) states that n=20 and p=0.10 (or equivalent), and (4) in part (ii) correctly calculates the expected value as 2 songs and provides supporting work for the calculation (e.g., np=20(0.10)=2).
1.0000pts
B_PThe response satisfies only two of the four components required for an essentially correct part B.
0.5000pts
C_EThe response satisfies all four of the following components for part C: (1) in part (i) provides the correct probability of 0.133 (or a probability consistent with the correct binomial calculation for P(X ≥ 4) with n=20 and p=0.10), (2) in part (i) shows work supporting the correct probability (acceptable work includes a probability formula, calculator function notation with clearly defined arguments, graphical display with appropriate bars shaded, or random variable notation P(X ≥ 4) or 1−P(X ≤ 3) with identification of binomial parameters; calculator notation without a labeled boundary value does not satisfy this component), (3) in part (ii) indicates that there is not a strong reason to believe the selection process was not truly random, and (4) in part (ii) provides an explanation that correctly links the probability to the decision (e.g., the probability is high enough to be reasonably attributed to chance alone).
1.0000pts
C_PThe response satisfies only two or three of the four components required for an essentially correct part C.
0.5000pts
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q4
Question 4
4. A software application (app) lets users enter questions to receive answers in the form of images, texts, or videos. Research indicates that 22 percent of high school students in Country W use the app to help them with their homework at least once per week. Karen is an AP Statistics student in Country W at a high school that has more than 2,000 students. She believes the proportion of all students at her school who use the app to help them with their homework at least once per week is greater than the proportion for her country. To investigate her belief, she took a simple random sample of 130 students from her school and found that 38 of the sampled students use the app to help them with their homework at least once per week. Is there convincing statistical evidence, at a 0.05 significance level, to support Karen's belief? Justify your answer with the appropriate inference procedure.
Rubric Criteria (6)
Section1_EThe response satisfies all four of the following components for Section 1: (1) identifies a one-sample z-test for a population proportion by name (e.g., "one-proportion z-test" but not merely "one-sample z-test") or by the correct formula using z (not t) (identifying the correct test by name but also stating an unreasonable formula does not satisfy this component), (2) states the correct equality for the null hypothesis with the value 0.22 (e.g., H0: p = 0.22 or H0: p ≤ 0.22), (3) states the correct direction for the one-sided alternative hypothesis consistent with the null (e.g., Ha: p > 0.22), and (4) provides sufficient context for the parameter by including reference to the population proportion (or true proportion of students at Karen's high school) AND the sampling units (students) AND the response variable (using the application at least once per week). Context may be satisfied in the hypotheses, parameter definition, or conclusion; referring to the sample proportion using p̂ (unless defined as the population proportion) does not satisfy component 4. A correctly identified one-sample z-interval for a population proportion may satisfy component 1, and component 4 is satisfied if the response indicates it is a confidence interval for the true proportion.
1.0000pts
Section1_PThe response satisfies three of the four components required for an essentially correct Section 1.
0.5000pts
Section2_EThe response satisfies all four of the following components for Section 2: (1) checks the independence condition by referring to the random sample of 130 students and indicating that 130 is less than or equal to 10% of 2,000 (i.e., 130 ≤ 0.10N) or the total population size (minimally acceptable phrasing includes "random sample - check" or "SRS - check"; implying random assignment or only stating "random - check" is insufficient), (2) checks that the sample size is large enough to support the assumption that the sampling distribution of p̂ is approximately normal by verifying that the number of expected successes and expected failures are at least 10 through calculations such as np0 = 130(0.22) = 28.6 and n(1−p0) = 130(0.78) = 101.4 (a direct comparison against 5 or 10 using actual observed values 38 and 92 or formulas with values inserted is acceptable; n > 30 is not appropriate), (3) correctly reports the value of the z-statistic (approximately 1.99; correct work with an arithmetic or transcription error satisfies this component; inputting correct values but computing incorrectly also satisfies this component), and (4) reports the value for the correct p-value consistent with the test statistic and the procedure stated in Section 1 (approximately 0.023) OR compares the test statistic to an appropriate critical value (e.g., z > 1.645). Using the sample proportion in the standard error satisfies component 4 but not component 3. If a one-sided 95% confidence interval is correctly calculated as (0.227, ∞) or a two-sided 90% confidence interval as (0.227, 0.358), component 3 is satisfied.
1.0000pts
Section2_PThe response satisfies only two or three of the four components required for an essentially correct Section 2.
0.5000pts
Section3_EThe response satisfies both of the following components for Section 3: (1) provides a correct comparison of the p-value to alpha (e.g., the p-value is less than alpha) and provides a correct decision about the null and/or alternative hypothesis (the comparison may also be made by comparing the test statistic to an appropriate critical value; an explicit decision is not required; the decision may be implied within the conclusion statement; statements equivalent to "accept the null hypothesis" do not satisfy this component; if an explicit decision is stated and is inconsistent with the conclusion, component 1 is not satisfied), and (2) states a conclusion in context, consistent with and in terms of the alternative hypothesis, using nondefinitive language (e.g., "there is convincing statistical evidence that the population proportion of students at Karen's high school that use the application at least once per week is greater than 0.22"). Context must reference proportion, students (may be implied), and using the application; definitive language such as "proves" or "accepts the alternative" does not satisfy component 2. If components 1 and/or 2 are satisfied and the response provides an incorrect interpretation of the p-value, the criterion is not satisfied.
1.0000pts
Section3_PThe response satisfies only one of the two components required for an essentially correct Section 3.
0.5000pts
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q5
Question 5
5. According to a 2017 national survey in Country B, the mean number of bedrooms in newly built houses was 2.9. Rodney, a researcher, believes the mean number of bedrooms in newly built houses in the country was different in 2024 than it was in 2017. To investigate his belief, he took a large random sample of newly built houses in Country B in 2024 and recorded the number of bedrooms in each house. The distribution of the number of bedrooms for the sampled houses is summarized in the table. Distribution of the Number of Bedrooms for the Houses Sampled in 2024 Number of Bedrooms | 1 | 2 | 3 | 4 | 5 | 6 Proportion of Houses | 0.12 | 0.22 | 0.28 | 0.22 | 0.14 | 0.02 A. i. A house from the sample will be selected at random. What is the probability that the house had fewer than 3 bedrooms? Show your work. ii. What is the mean number of bedrooms for the sample of newly built houses in 2024? Show your work. B. Rodney will use a one-sample t-test for a population mean to test his belief. i. In the context of Rodney's investigation, state the hypotheses for the test. ii. Explain, in context, what a Type I error would be for Rodney's hypothesis test. C. A different researcher, Keisha, suggests using a confidence interval to investigate whether the mean number of bedrooms in newly built houses in 2024 in Country B was different from 2.9. Assume the conditions for inference have been met. Using Rodney's data, Keisha calculated a one-sample 97 percent confidence interval to estimate the population mean as (3.01, 3.19). Based on the confidence interval, what conclusion can be made for Rodney's hypothesis test in part B at α = 0.03? Justify your answer.
Rubric Criteria (6)
A_EThe response satisfies at least three of the following four components for part A: (1) in part (i) correctly calculates the probability that a randomly selected house had fewer than 3 bedrooms as 0.34, (2) in part (i) provides supporting work or justification for the probability calculation (e.g., P(X < 3) = P(X = 1) + P(X = 2) = 0.12 + 0.22 = 0.34), (3) in part (ii) correctly calculates the mean number of bedrooms as 3.10, and (4) in part (ii) provides supporting work or justification for the mean calculation (e.g., showing at least two terms such as 1(0.12) + 2(0.22) + ... or stating the appropriate formula for the mean of a discrete random variable).
1.0000pts
A_PThe response satisfies only two of the four components required for an essentially correct part A.
0.5000pts
B_EThe response satisfies all four of the following components for part B: (1) in part (i) states the correct equality for the null hypothesis with the value 2.9 (e.g., H0: μ = 2.9), (2) in part (i) states the correct two-sided alternative hypothesis consistent with the null (e.g., Ha: μ ≠ 2.9), (3) in part (i) provides sufficient context for the parameter by including a reference to the population mean (or true mean), the response variable (bedrooms), and the sampling units (newly built houses in 2024 from Country B) (referring to the sample mean using x̄ or referring to "mean number of bedrooms" without "population/true/all" does not satisfy this component unless defined as the population mean; using notation μ may satisfy the population aspect), and (4) in part (ii) correctly defines a Type I error in context as determining that the population mean number of bedrooms in newly built houses in 2024 from Country B is not equal to 2.9 when it is in fact 2.9 (referring to "bedrooms" or "rooms" satisfies the context aspect).
1.0000pts
B_PThe response satisfies only three of the four components required for an essentially correct part B.
0.5000pts
C_EThe response satisfies both of the following components for part C: (1) states a conclusion consistent with and in terms of the alternative hypothesis using nondefinitive language (e.g., "there is convincing statistical evidence that the population mean number of bedrooms in newly built houses in 2024 from Country B is not equal to 2.9" or "there is evidence to support the alternative"), and (2) provides a justification for the conclusion by indicating that 2.9 is not contained within the confidence interval. A response that only provides an interpretation of the confidence interval without a conclusion and justification is scored incorrect; a definitive response that states the average is exactly 3.10 or any other number does not satisfy component 1.
1.0000pts
C_PThe response satisfies only one of the two components required for an essentially correct part C.
0.5000pts
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q6
Question 6
6. Stefan, a psychologist, conducted a study to investigate the effect of time of day on reading comprehension in children. One hundred children volunteered, with their parents' consent, to participate in the study. Fifty of the children were randomly assigned to read a story at 9 a.m. and then answer 25 questions about it. The remaining 50 children were assigned to read the same story at 3 p.m. and answer the same 25 questions. The reading comprehension for each child was measured by a reading score, which was determined by the number of questions that were answered correctly about the story. Stefan is interested in comparing the mean reading scores for the two times of day. Table 1 shows the results of Stefan's study. Table 1: Summary Statistics of Reading Scores | | n | Mean | Standard Deviation | |---|---|---|---| | 9 a.m. | 50 | 15.2 | 4.12 | | 3 p.m. | 50 | 17.9 | 4.43 | Stefan found the conditions for inference were met and conducted a two-sample t-test for the difference in two population means. Let $\mu_{\mathrm{AM}}$ represent the mean reading score for all children, similar to those in the study, who would read the story at 9 a.m. Let $\mu_{\mathrm{PM}}$ represent the mean reading score for all children, similar to those in the study, who would read the story at 3 p.m. Stefan's hypotheses are as shown. $$H_0: \mu_{\mathrm{AM}} = \mu_{\mathrm{PM}}$$ $$H_a: \mu_{\mathrm{AM}} \neq \mu_{\mathrm{PM}}$$ A. The p-value for Stefan's hypothesis test was 0.002. State an appropriate conclusion, at the 5 percent significance level, for Stefan's test in the context of the investigation. Justify your answer. B. Explain why it was appropriate for Stefan to conduct a two-sample t-test for the difference in two population means instead of a paired t-test for the population mean difference. C. Researchers are usually interested in the practical importance of their results as well as the statistical significance of the hypothesis test. The practical importance of the results indicates whether the observed results are meaningful in real life. For example, in an investigation of the heights of two groups of students, a difference in the two group means of 3.8 inches is much more meaningful, or has more practical importance, than a difference in the two group means of only 0.2 inches. One indicator of practical importance is effect size. A common method for measuring effect size for the difference in two group means is Cohen's d coefficient. Cohen's d coefficient compares the absolute value of the difference in the means of the two groups to the pooled variability of the observed data values from the two groups. Cohen's d coefficient can be calculated using $d = \frac{|\bar{x}_1 - \bar{x}_2|}{s_p}$, where $s_p$ represents the pooled standard deviation, $\bar{x}_1$ represents the sample mean for the first group, and $\bar{x}_2$ represents the sample mean for the second group. When the sizes of the groups are equal, $s_p$ is calculated as $s_p = \sqrt{\frac{s_1^2 + s_2^2}{2}}$, where $s_1$ represents the sample standard deviation for the first group and $s_2$ represents the sample standard deviation for the second group. Consider the summary statistics from Stefan's study in Table 1. i. Calculate Cohen's d coefficient for Stefan's study. Show your work. ii. Higher values of Cohen's d indicate greater practical importance and lower values of Cohen's d indicate less practical importance. Typically, we use the intervals listed in Table 2 to help interpret practical importance. Table 2: Guidelines for Interpreting Cohen's d Coefficient | Cohen's d Coefficient | Practical Importance | |---|---| | $0 \le d \le 0.20$ | Not very meaningful in real life | | $0.20 < d < 0.80$ | Somewhat meaningful in real life | | $d \ge 0.80$ | Very meaningful in real life | Based on your answer to part C (i) and the information in Tables 1 and 2, describe the practical importance of Stefan's results, in context. D. Suppose the results of Stefan's study, summarized in Table 1, instead had a standard deviation for the 9 a.m. reading scores, $s_1$, and a standard deviation for the 3 p.m. reading scores, $s_2$, that were both greater than 4.43. Assume the group sample sizes and the means are not changed. i. Would the Cohen's d coefficient in this new situation be smaller than, larger than, or the same as the Cohen's d coefficient calculated in part C (i)? Explain your answer. ii. Does the Cohen's d coefficient described in part D (i) indicate that Stefan's observed difference in the means in the new situation would have more practical importance than, less practical importance than, or the same practical importance as what was originally determined in part C (ii)? Explain your answer. STOP END OF EXAM
Rubric Criteria (8)
A_EThe response satisfies both of the following components for part A: (1) provides a correct comparison of the p-value to alpha (e.g., the p-value of 0.002 is less than the level of significance of 0.05) and provides a correct decision about the null and/or alternative hypothesis (the decision may be implied within the conclusion statement; an explicit decision inconsistent with the conclusion does not satisfy this component; comparing the test statistic to an appropriate critical value such as t > 1.985 with df ≈ 97.489 or t > 2.01 with df = 49 satisfies the comparison requirement), and (2) states a conclusion in context, consistent with and in terms of the stated alternative hypothesis using nondefinitive language, with reference to means, the groups (9 a.m. and 3 p.m.), the sampling units (children), and the variable of interest (reading score). Definitive language such as "proves" or "accepts the alternative" does not satisfy component 2. If components 1 and/or 2 are satisfied and the response provides an incorrect interpretation of the p-value, the criterion is not satisfied.
1.0000pts
A_PThe response satisfies only one of the two components required for an essentially correct part A.
0.5000pts
B_EThe response satisfies both of the following components for part B: (1) states that the two-sample t-test is appropriate because the groups of children are independent or because the groups of children were not paired in a meaningful way, and (2) explains why the groups are independent instead of paired, either by referencing the use of random assignment of the 100 children to the two groups or by providing an explanation that clearly separates the two situations, such as an example of how the data could have been paired (e.g., each child reading at both times, or twins). Stating that the groups are independent solely because one group was in the morning and one in the afternoon or because they received different treatments does not satisfy component 2.
1.0000pts
B_PThe response satisfies only one of the two components required for an essentially correct part B, or states that a two-sample t-test is appropriate because different samples were used but does not explicitly state that the children in the two samples were not paired in a meaningful way.
0.5000pts
C_EThe response satisfies both of the following components for part C: (1) in part (i) correctly calculates the value of Cohen's d (approximately 0.63) with work shown for Cohen's d (showing work for the pooled standard deviation is not required; an arithmetic or transcription error can be ignored if correct work is shown), and (2) in part (ii) indicates the correct level of practical importance that is consistent with the calculated Cohen's d (e.g., somewhat practical or meaningful in real life for d ≈ 0.63; a negative Cohen's d indicating "not very meaningful" may satisfy component 2).
1.0000pts
C_PThe response satisfies only one of the two components required for an essentially correct part C.
0.5000pts
D_EThe response satisfies all three of the following components for part D: (1) in part (i) states that the value of Cohen's d would be smaller, (2) in part (i) provides a reason for the change that includes a correct reference to how Cohen's d will change based on an increase in the pooled standard deviation (e.g., if both standard deviations were greater than 4.43, the pooled standard deviation would be greater than 4.28, and with a larger denominator and same numerator, Cohen's d would decrease; if only the pooled standard deviation was calculated in part C with no Cohen's d value, explaining that larger standard deviations result in an increased pooled standard deviation and therefore a lower effect size may satisfy this component), and (3) in part (ii) states that the decrease in Cohen's d would indicate there was less practical importance than the original study results (using Table 2 to indicate the category may be lower or unknown is acceptable).
1.0000pts
D_PThe response satisfies only two of the three components required for an essentially correct part D.
0.5000pts
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This material is the intellectual property of College Board, is not owned by GradeThis, and is shown here for ease of use and demonstration purposes.