Answer :
Final answer:
To convert the F-statistic to a t-statistic, take the square root of the F-value. For the given F-statistic F(1,30)=6.25, p=0.02, the correct t-test statistic is t(30) = 2.5, p = 0.02.
Explanation:
The question is asking to convert an F-statistic from an analysis of variance (ANOVA) test to a corresponding t-test statistic for a between-subjects study. The F-statistic provided (F(1,30)=6.25, p=0.02) indicates that there is one degree of freedom for the numerator and 30 degrees of freedom for the denominator. The key to converting an F-statistic to a t-statistic when the numerator degree of freedom is 1 is to take the square root of the F-value. Therefore, the t-test statistic is the square root of 6.25, which is roughly 2.5.
The degrees of freedom in a t-test are the same as the denominator in the F-test, which in this case is 30. Therefore, the correct conversion of the F-statistic to a t-test statistic is t(30) = 2.5. The p-value remains the same because the significance of the test is not affected by this conversion.
Correct answer: C) t(30) = 2.5, p = 0.02
