1. It has been claimed that flattening ("rolling") the barrel of a graphite baseball bat can stretch the fibers and result in a pitched baseball being returned faster than with a regulation bat. This was a controversial topic dur- ing the 2009 baseball College World Series. Assume that data file XR11013 describes the results of a controlled test measuring the return speeds of balls pitched to a flattened bat and a regulation bat, respectively. Based on these sample results, and using a suitable one-tail test at the 0.05 level, was the mean return speed for the flattened bat significantly greater than for the regulation bat? Identify and interpret the p-value for the test. Source: Andy Gardiner, "NCAA on Guard for ‘Rolled' Bats," USA Today, June 17, 2009, p. 8C.
2. Comparing the number of Facebook "friends" for men and women, observers have speculated about whether the mean number of friends could be the same for each group. Assume that data file XR11014 lists the number of Facebook friends for independent samples of male and female Facebook users. Based on the results of a two-tail test at the 0.05 level, comment on whether the difference between the sample means could have simply occurred by chance. Identify and interpret the p-value for the test.