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 2.25. the critical value (tcv) was 2.05. the standardized difference (t) between population means is greater than the critical value (tcv) and is significant. the standardized difference (t) between population means is greater than the critical value (tcv) and is not significant. the standardized difference (t) between sample means is greater than the critical value (tcv) and is significant. the standardized difference (t - tcv) between population and sample means is (2.25 - 2.05) 0.20, which is not significant. the standardized difference (t) between sample means is greater than the critical value (tcv) and is not significant.

Explanation:

In a t - test, we compare the calculated t - value (standardized difference) with the critical t - value (\(t_{cv}\)). If \(t>t_{cv}\), the difference is significant. Here, \(t = 2.25\) and \(t_{cv}=2.05\) (\(2.25>2.05\)). Also, the t - test is used to test the difference between sample means (not population means as we are using sample data to make inferences).

Answer:

The standardized difference (t) between sample means is greater than the critical value (\(t_{cv}\)) and is significant.