Two-Tailed Test

In statistical hypothesis testing, what is the primary function of a critical value?

A researcher is conducting a psychology study and needs to use a critical value to determine if their results are significant. Arrange the following steps in the correct logical sequence for this statistical decision-making process.

A psychologist investigating the relationship between physical exercise and mental clarity calculates a test statistic of 1.82. If the critical value for significance in this study is 1.96, the researcher should conclude that the results are statistically significant and reject the null hypothesis.

In psychology research, statistical decisions depend on where the threshold for significance is placed. Analyze how different modifications to a study's design or criteria affect the critical value and match each change to its corresponding impact on that threshold.

In psychological research, which two statistical components are required to determine the specific critical value used for a hypothesis test?

In null-hypothesis significance testing, the critical value is calculated directly from the study's collected sample data, meaning its numerical value will change based on the empirical results of the study.

A researcher reports that their findings are statistically significant because their calculated test statistic reached $2.15$. A skeptical reviewer evaluates this claim and notes that if the researcher had adopted a more stringent significance level (such as $\alpha = .01$ instead of $\alpha = .05$), the numerical boundary known as the _____ would have been set at a more extreme point (such as $2.58$ instead of $1.96$), meaning the same results would no longer be considered significant.

A researcher reports the following test statistics alongside their corresponding critical values from a psychology study. Match each result to the correct statistical decision about the null hypothesis.

A researcher conducts a two-tailed one-sample t-test with 13 degrees of freedom and obtains t = 2.20. The critical value at $\alpha = .05$ is $\pm2.160$. Because the computed t score exceeds the critical value, the researcher can conclude that the p value for this result is _____ .05, which is why the result is deemed statistically significant and the null hypothesis is rejected.

A peer reviewer is judging whether a researcher correctly used a critical value to justify rejecting the null hypothesis in a one-sample t-test. Arrange the following reviewer criteria in the logical order they should be applied to render a sound and well-supported judgment.

Define a critical value in null hypothesis significance testing. In your response, recall the two primary statistical components used to derive a critical value, and describe what decision is made regarding the null hypothesis when a calculated test statistic falls beyond this threshold.

Based on the provided case, explain what the critical value of $\pm2.160$ represents in terms of the probability of obtaining extreme t-scores if the null hypothesis is true. Then, decide what statistical action the researcher should take regarding the null hypothesis, justifying your decision by comparing the calculated t-score to the critical value.

A cognitive researcher conducts an ANOVA and computes an F-ratio of $3.12$. The critical value of F for the study's degrees of freedom (2 and 21) at $\alpha = 0.05$ is $3.467$. Apply these values to determine whether the result is statistically significant, and state what decision the researcher should make regarding the null hypothesis.