In a one-sample $t$-test, which statement best explains the relationship between the sample size ($N$) and the degrees of freedom ($df$)?

A team of researchers is preparing to analyze data from several different psychology studies using one-sample $t$-tests. Match each research scenario's sample size ($N$) with the correct degrees of freedom ($df$) required for the statistical analysis.

A psychology researcher is evaluating how a change in sample size affects the statistical precision of a one-sample $t$-test. Arrange the following components in the logical order that describes how an increase in participants ($N$) alters the degrees of freedom and the resulting probability model.

A psychology researcher conducting a one-sample $t$-test with a sample of 28 students ($N = 28$) argues that using 28 degrees of freedom ($df = 28$) to determine the shape of the probability model is a valid methodological adjustment to increase the precision of their findings. This researcher's evaluation of the statistical requirements is scientifically sound.

In a one-sample $t$-test, which statistical value determines the exact shape of the $t$ distribution?

In a one-sample $t$-test, two different research studies with different sample sizes ($N$) will analyze their data using the exact same shape of the $t$ distribution.

For a one-sample $t$-test, the degrees of freedom are calculated as the sample size minus _____.

A researcher reports the degrees of freedom used in each one-sample $t$-test. Match each reported $df$ value to the sample size ($N$) that would produce it.

A researcher reports that a one-sample $t$-test was conducted using a $t$-distribution with 23 degrees of freedom. A colleague replicates the study with exactly twice the original sample size. The replication's $t$-test will use a $t$-distribution with _____ degrees of freedom.

A student peer-reviewing a classmate's one-sample $t$-test report must judge whether the reported degrees of freedom are correct. Arrange the following steps in the order the student should follow to conduct this evaluation.

State the formula used to calculate the degrees of freedom ($df$) for a one-sample $t$-test, define what the variable $N$ represents, and recall how the degrees of freedom relate to the $t$ distribution.

Explain why the assistant's assertion is incorrect, how the actual shape of the distribution is determined, and calculate the specific degrees of freedom value for this sample.

An educational psychologist is analyzing test scores for a class of 30 students ($N = 30$) using a one-sample $t$-test. Apply the formula for degrees of freedom to determine the $df$ value they must report, and state what this value specifies about the statistical model.