An experiment was conducted to compare mean reaction time to two types of traffic signs: prohibitive (no left turn) and permissive (left turn only). Ten subjects were included in the experiment. Each subject was presented 40 traffic signs, 20 prohibitive and 20 permissive, in random order. The mean time to reaction and the number of correct actions were recorded for each subject. The mean reaction times to the 20 prohibitive and 20 permissive traffic signs for each of the ten subjects are reproduced in the following table.
Mean Reaction Times (ms)for
20 Traffic Signs
Subject Prohibitive Permissive
1 824 702
2 866 725
3 841 744
4 770 663
5 829 792
6 764 708
7 857 747
8 831 685
9 846 742
10 759 610
a. Explain why this is a matched-pairs experiment and give reasons why the pairing should be useful in increasing information on the difference between the mean reaction times to prohibitive and permissive traffic signs.
b. Do the data present sufficient evidence to indicate a difference in mean reaction times to prohibitive and permissive traffic signs? Test using α=.05.
c. Find and interpret the approximate p-value for the test in part (b).
d. Find a 95% confidence interval for the difference in mean reaction times to prohibitive and permissive traffic signs.