1. Do children diagnosed with attention deficit/hyperactivity disorder (ADHD) have smaller brains than children without this condition? Brain scans were completed for 152 children with ADHD and 139 children of similar age without ADHD. The mean brain size for the 152 children with ADHD was 1059.4 mL with a standard deviation of 117.5 mL. The mean brain size for the 139 children without ADHD was 1104.5 mL with a standard deviation of 111.3 mL.The standard deviation of a simulated null distribution of 1,000 differences in sample mean brain sizes was 13.4 mL. Calculate the standardized statistic for a test of two means (ADHD - Without ADHD).

2. An article that appeared in the British Medical Journal (2010) presented the results of a randomized experiment conducted by researcher Jeremy Groves, whose objective was to determine whether the weight of his bicycle could affect his travel time to work. On each of 56 days (from mid-January to mid-July 2010), Groves tossed a 1 coin to decide whether he would be biking to work on his carbon frame (lighter) bicycle that weighed 20.9 lbs or on his steel frame (heavier) bicycle that weighed 29.75 lbs. He then recorded the commute time (in minutes) for each trip.Here are the summary statistics for his data:

Bike Type	Sample size	Sample average	Sample SD
Carbon frame (lighter)	26	108.34 min	6.25 min
Steel frame (heavier)	30	107.81 min	3.89 min

Use the Theory-Based Inference applet to find the theory-based p-value for the appropriate test of two means.