Two-Tailed $t$-Test

One-Tailed $t$-Test

What do critical values of $t$ represent in a $t$ distribution?

In a hypothesis test, if a calculated $t$ score falls beyond the established critical values of $t$, the score is considered to be in the extreme tail of the distribution, which leads the researcher to reject the null hypothesis.

A psychology researcher is conducting a study using a two-tailed $t$-test with $24$ degrees of freedom ($df$) and an alpha level ($\alpha$) of $.05$. Based on these parameters, the critical values are $\pm 2.064$. Match each calculated $t$-statistic to the correct statistical conclusion regarding the null hypothesis.

A psychology researcher is evaluating how different alpha levels ($\alpha$) and sample sizes (expressed as degrees of freedom, $df$) influence the boundaries of a two-tailed $t$-test. Arrange the following scenarios in order based on the magnitude of their critical values, starting with the scenario that results in the largest absolute critical value (the most extreme threshold) and ending with the smallest absolute critical value (the least extreme threshold).

Imagine you are designing a standardized 'Statistical Rigor' manual for a psychology department. Your goal is to create a set of guidelines for choosing critical values of $t$ that maximize the stringency of hypothesis tests, making the boundaries for rejecting the null hypothesis as extreme (furthest from zero) as possible. Which set of selection criteria correctly synthesizes the parameters needed to create these high-stringency thresholds?

A psychology researcher is preparing to conduct a hypothesis test. Match each statistical component with its role in establishing the boundaries used to evaluate the results.

Imagine you are moving outward from the center of a $t$ distribution (where $t = 0$) toward one of the extreme tails. Arrange the following components in the order you would encounter them according to the logic of critical values.

A psychology researcher calculates an obtained $t$ score of $2.060$. Given that the critical value for the study is set at $2.064$, the researcher decides to reject the null hypothesis, arguing that the result is 'close enough' to the threshold. Based on the objective criteria defined by the critical values of $t$, this researcher's conclusion is _____.

Two researchers both conduct two-tailed $t$-tests at $\alpha = .05$, but Researcher A has $9$ degrees of freedom (critical value $\approx \pm 2.262$) while Researcher B has $24$ degrees of freedom (critical value $= \pm 2.064$). If both researchers obtain a calculated $t$ score of $2.10$, only Researcher B would reject the null hypothesis.

A research team conducting a two-tailed $t$-test decides to lower their alpha level from $.05$ to $.01$ to reduce the risk of a false positive finding. Evaluating this decision: lowering the alpha level causes the critical values of $t$ to move _____ from zero, meaning a more extreme obtained $t$ score is required before the null hypothesis can be rejected.

Define critical values of $t$ and explain what factors determine them, according to the provided text. Describe what it means for a calculated $t$ score to fall beyond a critical value in terms of hypothesis testing.

Based on the provided case details, explain what the calculated $t$ score of $2.500$ indicates about the location of the score in the $t$ distribution, and state what decision the student should make regarding the null hypothesis.

A researcher is conducting a study with $24$ degrees of freedom and an alpha level of $.05$. If they calculate a $t$ score of $-1.850$, apply the rules of critical values to determine whether this score falls in the extreme tail and if they should reject the null hypothesis.