Degrees of Freedom (One-Sample t-Test)

Example of Finding a p-Value for a t Score

What does the t distribution specifically illustrate?

Based on the provided image of the distribution of t scores, match each mathematical characteristic with its conceptual meaning in psychological research.

A researcher is evaluating potential results from a study on how caffeine affects memory. Based on the provided image of the distribution curve and assuming the null hypothesis is true, arrange the following possible scores in order from the MOST likely to occur to the LEAST likely to occur.

In a $t$ distribution, an observed $t$ score of $+0.2$ will yield a larger $p$-value than a score of $-3.5$ because the distribution's unimodal shape and center at zero mean that values closer to the mean represent a larger proportion of results expected if the null hypothesis is true.

A researcher is constructing a set of four hypothetical sample results ($t$ scores) to 'create' a visual model that perfectly aligns with the properties shown in the provided image of the $t$ distribution. They have already generated two scores: $-3.1$ and $+0.5$. To complete the set so that it is both perfectly symmetrical and centered at precisely $0$, which two additional $t$ scores must they generate?

A researcher argues that a calculated $t$ score of $-4.2$ is 'less extreme' than a score of $+2.5$ because the negative sign makes it a 'smaller' number. This reasoning is flawed because the $t$ distribution is _____, meaning that a score's distance from $0$ — not its sign — determines how extreme it is relative to the null hypothesis.

The $t$ distribution illustrates the spread of possible $t$ scores that researchers would expect to observe if the _____ were entirely true.

A researcher obtains a $t$ score of $-2.3$ and uses the $t$ distribution to evaluate how consistent this result is with the null hypothesis. They conclude that $-2.3$ is just as extreme as $+2.3$ and would therefore produce the same $p$-value. This conclusion is correct.

Match each feature of the $t$ distribution to the statement that correctly explains its role in hypothesis testing.

A student argues that a $t$ score of $-0.4$ provides stronger evidence against the null hypothesis than a $t$ score of $+3.1$ because the negative sign indicates an 'opposite' result. Arrange the following evaluative steps in the correct order to judge whether this reasoning is valid.

Describe the graphical shape, the exact numerical value of the center, and the overall purpose of the $t$ distribution in psychological research.

Explain why the $t$ distribution is centered precisely at $0$ in this context, and explain how the researcher uses this curve to determine the $p$-value for their computed $t$ score.

If a researcher calculates a $t$ score of $+2.0$ in a psychological study, how do they apply the $t$ distribution to find the corresponding $p$-value, and what does this $p$-value represent?