Egbert Techster is very serious about winning this year's All-American Soap Box Derby competition. Since there is no wind-tunnel time available at the aerospace firm where his father works, Egbert is using a local hill to test the effectiveness of an aerodynamic design change. In 10 runs with the standard car, the average time was 22.5 seconds, with a standard deviation of 1.3 seconds. With the design change, 12 runs led to an average time of 21.9 seconds, with a standard deviation of 0.9 seconds.
Assuming normal populations with equal standard deviations, use the 0.10 level in helping Egbert determine whether the modifications are really effective in improving his racer's speed. Using the appropriate statistical table, what is the approximate p-value for this test?