Research suggests that the pressure of being timed may interfere with performance on tests that involve mathematical problems. A fictional study was conducted with 30 6th graders. First, the 6th graders were given a math test that contained 50 problems and were told that they had only one hour to complete it (Timed Condition). The same 6th graders were later given a math test that contained 50 problems and were told that they could have as much time, as needed, to complete the test (Unlimited Time Condition). The total number of correct answers for each 6th grader was then calculated for each condition. Then, for each student, the difference between the twoscores (Timed-Untimed) was calculated. The researchers hypothesized that the 6th graders would get fewer correct answers, when they took the test with a time limit, as compared to
when they had unlimited time.
[Tramo MJ, Loftus WC, Green RL, Stukel TA, Weaver JB, Gazzaniga MS. Brain Size, Head Size, and IQ in Monozygotic Twins. Neurology 1998; 50:1246-1252.]
If �1and �2represent the number of correct answers during the Timed Condition and the
Unlimited Time Condition, respectively, and let �d be the mean of the differences in the
number of correct answers (Timed-Untimed) of all 6th graders. Which are the
appropriate null and alternative hypotheses?A. H0: �d = 0, Ha: �d > 0
B. H0: �d = 0, Ha: �d < 0
C. H0: �d < 0, Ha: �d = 0
D. H0: �1- �2 = 0, Ha: �1 - �2 < 0
E. Both (B) and (D) are correct.