1. Operational definition (1): Clear, observable measure (e.g., “number of words correctly recalled out of 30 within 5 minutes”). Must be specific to this study.
2. IV & DV (2): IV = sleep condition (8h vs 4h). DV = memory performance as defined above.
3. Random assignment (1): Explains that it equalizes preexisting differences between groups, reducing confounds and allowing causal inference about sleep amount.
4. Confound + control (1): Names a plausible confound (e.g., caffeine, prior sleep debt, study time, time of testing, noise) and describes a control (e.g., prohibit caffeine, standardize study time/time of day, quiet room).
5. p = .02 interpretation (1): If no true effect, there’s ~2% chance of a difference this large just by chance; therefore results are statistically significant at α=.05.
6. Similar SDs (1): Score variability/spread is comparable in both groups; differences are in the means, not dispersion.

Note: Credit requires application to the given sleep study, not generic definitions alone.

(1) I would operationally define memory performance as the number of words correctly recalled out of 30 within a 5-minute recall period. (2) The independent variable is the sleep condition (8 hours vs 4 hours), and the dependent variable is the recall score as defined. (3) Random assignment puts students into conditions by chance, which helps equalize prior differences (like motivation or baseline memory) across groups, so any difference in recall can be attributed to sleep amount. (4) A potential confound is caffeine intake; to control it, the researcher could prohibit caffeine for 12 hours before testing for all students. (5) A p-value of .02 means that if sleep had no real effect, there is a 2% probability of seeing a difference in recall as large as the one found just by chance, so the result is statistically significant at the .05 level. (6) Similar standard deviations indicate that score spread was about the same in both groups; the main difference is in the average recall, not in variability.

“Memory performance is how well they remember.” (Too vague; not operational.) “We randomly selected students so it proves causation.” (Confuses random sampling with random assignment.) “p=.02 means there’s a 2% chance the hypothesis is true.” (Incorrect; p is about data under the null.)

1. r interpretation (1): Negative, moderately strong relationship; as minutes increase, mood tends to decrease.
2. No causation (1): Could be third variables (stress, sleep), reverse causation, or measurement issues; correlation does not control confounds.
3. Experiment design (2): IV = assigned social media limit/condition; DV = mood rating measure; random assignment of participants to conditions; standardized procedures (e.g., 1-week restrictions).
4. Blind procedure (1): Explains how single-blind (participants unaware of hypothesis/condition specifics) or double-blind (including raters) reduces expectancy bias/demand characteristics.
5. Mean vs median with outlier (1): Median preferred because the mean is pulled upward by extreme outliers like 720 minutes.

(1) r = −.60 indicates a moderately strong negative relationship: students with more social media minutes tend to report lower mood. (2) Correlation cannot establish causation because other factors like stress or lack of sleep might cause both high use and low mood, and the data do not control those confounds. (3) In an experiment, I would randomly assign students to either a low-use condition (≤30 minutes/day) or a high-use condition (≥120 minutes/day) for one week, then measure mood with the same 1–7 scale; random assignment helps equalize groups so differences can be attributed to use. (4) To reduce expectancy effects, use a single-blind procedure where participants are told they are in a “digital habits study” without the specific hypothesis, and use blind raters who score mood surveys without knowing condition. (5) The median minutes is better because an extreme outlier (720 minutes) would distort the mean.

“r = −.60 means social media causes bad moods.” (Causation claim.) “I will randomly sample students into conditions.” (Needs random assignment.) “We’ll use the mean minutes even with extreme values.” (Ignores outlier sensitivity.)

1. z-score (2): Correct calculation: \( z = \frac{95-80}{10} = 1.5 \) (1 pt) and correct interpretation (≈1.5 SDs above the mean; Alex scored higher than most students) (1 pt).
2. Empirical rule (1): ~68% between −1 SD (70) and +1 SD (90) with justification referencing the normal curve rule.
3. p = .04 interpretation (1): Significant at α=.05; if no true effect, ~4% chance of a difference this large by random assignment; suggests the program may improve scores.
4. Confidence interval (1): If we repeatedly sampled, about 95% of such intervals would capture the true district mean; we are reasonably confident the mean lies between 78 and 82.
5. Replication (1): Repeating in more classes/schools checks that the effect is reliable and not a one-time fluke or due to unique class factors.

(1) z = (95-80)/10 = 1.5. Alex scored about 1.5 standard deviations above the mean, which places Alex higher than the majority of students. (2) Using the empirical rule, about 68% of scores fall within one SD of the mean, so roughly 68% score between 70 and 90. (3) With p = .04, the difference between the program and control classes is statistically significant at the .05 level, meaning that if the program had no real effect, we would see a difference this large only about 4% of the time by chance. (4) A 95% confidence interval of [78, 82] means we are reasonably confident the true district average is between 78 and 82; over many samples, 95% of such intervals would include the true mean. (5) Replication across additional classes and schools is important to make sure the benefit is reliable and not due to unique features of this one class or teacher.

“z = 1.5 means Alex is in the 100th percentile.” (Over-interpretation.) “p = .04 proves the program works.” (p-values don’t prove; they quantify how unusual the data are if the null were true.) “95% CI means 95% of students score between 78 and 82.” (That’s not what a CI means.)