1Cademy - One-Sample $$t$$-Test

Learn Before

Types of $t$ -Tests

Concept

One-Sample $t$ -Test

The one-sample $t$ -test is a statistical procedure used to compare a sample mean ( $M$ ) against a hypothetical population mean ( $\mu_0$ ). It is used to evaluate whether the sample likely comes from a population with that specific mean.

Updated 2026-05-16

Contributors are:

Who are from:

References

KPU Research Methods in Psychology - 4th American Edition

Tags

KPU

Research Methods in Psychology - 4th American Edition @ KPU

Match each type of t-test with the research scenario it is designed to analyze.
A researcher is comparing the average test scores of two separate groups of students: one group that studied in a quiet library and another group that studied with background music. Which variation of the $t$ -test is the most appropriate for this research design?
Using an independent-samples $t$ -test to analyze a research design where the same group of participants is measured in two different conditions is a structural error because it treats the scores as unrelated and fails to account for the systematic variance shared between the data points.
Arrange the logical evaluative steps in the correct sequence for a researcher to determine which specific variation of the $t$ -test is the most appropriate for their research design.
Imagine you are generating an integrated statistical plan for a multi-stage study on a new mindfulness intervention. Your research protocol requires the following three components:
1. A validation step to determine if your recruited sample's baseline stress scores differ significantly from the established national average.
2. An assessment of whether the participants' individual stress levels changed from the beginning to the end of the intervention.
3. A concluding comparison to see if the final stress levels of the intervention group differ from a separate group of participants who received a neutral control activity.
Which of the following designs demonstrates the correct synthesis of $t$ -test variations to fulfill this three-part plan in order?
In a research design using 'matched-pairs'—where different participants are paired based on a shared characteristic (like sibling status) and then split into two separate conditions—the appropriate statistical analysis is an independent-samples $t$ -test because the scores come from two different groups of people.
A researcher is evaluating different research designs to maximize internal validity by minimizing the influence of participant-level variability. Rank the following types of $t$ -tests based on the degree of control their associated designs provide over individual differences, from the highest degree of control to the lowest degree of control.
A clinical psychologist wants to know if the average depression score of her current patients significantly differs from a well-established national average score of 20 on a standard assessment scale. She collects data from 50 of her patients to compare their mean score against this national value. Which $t$ -test is most appropriate for this analysis?
Match each type of $t$ -test with the research scenario that best illustrates its specific application in psychology.
One-Sample $t$ -Test
A clinical psychologist measures the anxiety levels of 25 participants before they undergo a new relaxation therapy and then measures the anxiety levels of those same 25 participants again after the therapy is complete. To determine if there was a significant change in anxiety scores, the psychologist should perform a(n) _____ $t$ -test.
The three primary variations of the $t$ -test are the one-sample $t$ -test, the independent-samples $t$ -test, and the _____-samples $t$ -test.

Learn After

One-Sample $t$ -Test Formula
What is the primary purpose of a one-sample $t$ -test?
A clinical psychologist can use a one-sample $t$ -test to evaluate whether a sample of patients with a specific disorder has a different average anxiety score than the established national average for the general population.
A clinical psychologist wants to determine if the average sleep duration of 31 patients with a specific diagnosis differs from the general population mean of 7.0 hours. Match each statistical component of the one-sample $t$ -test to its correct value or description from this study.
A neuropsychologist is using one-sample $t$ -tests to compare cognitive scores from different patient groups to a known population mean. Assuming the sample mean ( $M$ ) is higher than the population mean ( $\mu_0$ ) in all groups, rank the following scenarios from the highest calculated $t$ -value (top) to the lowest calculated $t$ -value (bottom).
An experimental psychologist is critiquing a research report that mistakenly uses a one-sample $t$ -test to compare the average test scores of two separate and independent student groups. The psychologist points out that this is an improper application of the statistic because a one-sample $t$ -test is specifically designed to evaluate a single sample mean ( $M$ ) against a(n) ______ mean ( $\mu_0$ ).
A researcher is evaluating whether the average test score of a sample of students ( $M = 82$ ) is significantly different from the district-wide average of $75$ . Given that the researcher is comparing a single sample to a fixed value and lacks the population standard deviation, the most appropriate statistical procedure for this evaluation is a(n) ______.
What is the primary purpose of a one-sample $t$ -test?
A researcher would use a one-sample $t$ -test to determine whether the average memory score of a specific group of participants ( $M$ ) significantly differs from a known national average score ( $\mu_0$ ).
A social psychologist investigates whether the average level of 'community belonging' among students at a specific college differs from the national average score of 12.0. They survey a sample of 31 students and find a mean ( $M$ ) score of 14.5 with a standard deviation ( $s$ ) of 2.1. Match each numerical value from this study to its correct statistical role in a one-sample $t$ -test.
A psychologist is testing whether the average score on a new 'Resilience Scale' for a group of trauma survivors differs from the established general population mean of 50. Arrange the following steps in the logical order required to conduct and interpret a one-sample $t$ -test.
Hypotheses in a One-Sample $t$ -Test
Example of a One-Sample $t$ -Test

Learn Before

Related

Learn After