Purpose of Null Hypothesis Testing

Two Interpretations of a Statistical Relationship in a Sample

Example of Sampling Error

What does the term 'sampling error' refer to in the context of psychological research?

In a well-designed study, the fact that a sample result differs slightly from the true population value is typically due to sampling error rather than a mistake in the research process.

A social psychologist randomly selects 50 participants from a local community to measure their average social anxiety score and gets a result of 15. A second psychologist selects a different random sample of 50 people from the same community and gets a score of 17. The fact that these two averages are slightly different purely due to random chance is an example of ______.

A social psychologist studying stress in nurses knows the true average stress score for all nurses in the state is 45. In one study of 50 nurses, the average is 47. In another study of 50 nurses, the average is 43. Match each element of this research scenario to the statistical concept it represents.

A researcher finds that the average score in their random sample is $105$, while the known population parameter for that group is $100$. Arrange the following interpretations of this discrepancy from the most scientifically accurate (1) to the least scientifically accurate (4) based on the concept of sampling error.

Which term refers to the natural, random variability that occurs in a statistic from one sample to another, even when all samples are randomly drawn from the same population?

A researcher draws two random samples (Study A and Study B) from the same population and calculates their averages. Arrange the following steps to logically explain the difference between these averages using the concept of sampling error.

A developmental psychologist randomly draws two different samples of 50 children from the same local school district to measure their average screen time. Sample 1 has a mean screen time of $2.4$ hours per day, while Sample 2 has a mean of $2.8$ hours per day. Because these sample statistics are different and do not perfectly estimate the population parameter, the psychologist can conclude that a procedural mistake must have been made during the data collection of at least one sample.

A researcher is analyzing why the average anxiety scores differ between three randomly selected samples of college students drawn from the same campus population. Match each concept to its correct description in this research context.

A research evaluator reviews a report where two psychologists drew different random samples from the same population and got average scores of $7.2$ and $6.9$, respectively. The author of the report concludes that one of the psychologists must have made an error in data collection. The evaluator should judge this conclusion as incorrect because the difference between the sample statistics is likely due to _____, which is a natural and expected occurrence that does not imply a research mistake.

Purpose of Null Hypothesis Testing

Null Hypothesis Testing

What are the two mutually exclusive interpretations researchers must choose between when they observe a statistical relationship within a sample?

A researcher surveys 80 university students and finds a positive correlation between daily study hours and exam scores. According to the logic of statistical inference, it is a legitimate interpretation that no real relationship between study hours and exam scores exists in the broader student population, and that the correlation appeared in the sample solely because of chance variation in which individuals happened to be selected.

A researcher identifies a positive correlation between exercise and mood in a sample of 50 participants. Arrange the logical steps involved in analyzing this finding according to the two interpretations of statistical relationships.

You are designing a 'Standardized Results Template' for an undergraduate psychology lab. The template requires students to construct a 'Mutual Exclusivity' section for any observed correlation in their sample. Which of the following drafts provides the most accurate and complete construction of the two interpretations a student must present for a finding like $r = 0.35$?

Match each term regarding the two interpretations of an observed statistical relationship with its corresponding claim about the broader population.

A researcher finds that participants who slept 8 hours performed better on a logic task than those who slept 6 hours. When deciding whether to generalize this finding to the broader population, the researcher must consider whether the observed relationship is genuine or whether it is simply a(n) _____ of random sampling error.

A researcher finds that in a sample of 80 students, those who listened to classical music while studying scored 10% higher on a logic test than those who studied in silence. Match each statement to the correct conceptual interpretation of this sample result.

When a researcher observes a statistical relationship in a sample and concludes that it reflects a genuine relationship in the population, they are logically rejecting the interpretation that the result is merely an artifact of _____.