American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat. The league believes that replacing the pitcher, traditionally a weak hitter, with another player in the batting order produces more runs and generates more interest among fans. The data provided in the file Attendance 2016 include the average numbers of runs scored per game (Runs per game) by American League and National League teams for the 2016 season (www .baseball-reference.com).

a) Create an appropriate display of these data. What do you see?

b) With a 95% confidence interval, estimate the mean number of runs scored by American League teams.

c) With a 95% confidence interval, estimate the mean number of runs scored by National League teams.

d) Explain why you should not use two separate confidence intervals to decide whether the two leagues differ in average number of runs scored.

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American League National League Тeam Runs/game Team Runs/game Baltimore Orioles 4.59 Arizona Diamondbacks 4.64 Boston Red Sax 5.42 Atlanta Braves 4.03 Chicago White Sax 4.23 Chicago Cubs 4.99 Cleveland Indians 4.83 Cincinnati Reds 4.42 Detroit Tigers 4.66 Colorado Rockies 5.22 Houston Astros 4.47 Los Angeles Dodgers 4.48 Kansas City Royals 4.17 Miami Marlins 4.07 Los Angeles Angels 4.43 Milwaukee Brewers 4.14 Minnesota Twins 4.46 NY Mets 4.14 NY Yankees 4.20 Philadelphia Phillies 3.77 Oakland Athletics 4.03 Pittsburgh Pirates 4.50 Seattle Mariners 4.74 San Diego Padres 4.23 Таmpa Вay Rays 4.15 San Francisco Giants 4.41 Texas Rangers 4.72 St Louis Cardinals 4.81 Toronto Blue Jays 4.69 Washington Nationals 4.71