Question

a sample of chess players (x1) and checker players (x2) were given an iq test. the results of the iq tests were analyzed with a t - test. the standardized difference (t) was 2.02. the critical value (t_{cv}) was 2.05. the results are significant, so we reject the null hypothesis. we cannot make a conclusion on results (t - t_{cv}=-0.03) that are negative or not significant. the results are not significant, so we fail to reject the null hypothesis. the results are significant, so we fail to reject the null hypothesis. the results are not significant, so we reject the null hypothesis.

Explanation:

Step1: Understand t - test decision rule

In a t - test, if \(|t|\geq t_{cv}\), the results are significant and we reject the null hypothesis. If \(|t|\lt t_{cv}\), the results are not significant and we fail to reject the null hypothesis.

Step2: Compare \(t\) and \(t_{cv}\) values

Given \(t = 2.02\) and \(t_{cv}=2.05\). Calculate \(|t|=2.02\) and \(t_{cv} = 2.05\). Since \(2.02\lt2.05\) (i.e., \(|t|\lt t_{cv}\)).

Answer:

The results are not significant, so we fail to reject the null hypothesis.