The dataset BaseballHits gives 2010 season statistics for all Major League Baseball teams. We treat this as a sample of all MLB teams in all years. Computer output of descriptive statistics for the variable giving the batting average is shown:

(a) How many teams are included in the dataset? What is the mean batting average? What is the standard deviation?
(b) Use the descriptive statistics above to conduct a hypothesis test to determine whether there is evidence that average team batting average is different from 0.250. Show all details of the test.
(c) Compare the test statistic and p-value you found in part (b) to the computer output below for the same data:

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Descriptive Statistics: BattingAvg Variable N* Mean SE Mean StDev 0.00190 0.01039 0 0.25727 BattingAvg 30 Q1 Median Q3 Maximum Minimum 0.23600 0.24800 0.25700 0.26725 0.27600 One-Sample T: BattingAvg Test of mu = 0.25 vs not = 0.25 Variable Mean StDev BattingAvg 30 0.25727 0.01039 SE Mean 95% CI 0.00190 (0.25339, 0.26115) 3.83 0.001