Question

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. Below are the average numbers of runs score in American League and National League stadiums for the first half of the 2001 season. **American:** 11.1, 10.8, 10.8, 10.3, 10.3, 10.1,10.0, 9.5, 9.4, 9.3, 9.2, 9.2, 9.0, 8.3 **National:** 14.0, 11.6, 10.4, 10.3, 10.2, 9.5, 9.5, 9.5, 9.5, 9.1, 8.8, 8.4, 8.3, 8.2, 8.1, 7.9 (a) Create two box plots to display this data and comment on what you see. (b) Estimate the mean number of runs scored in American League games with a 95% CI. What concerns do you have about making a similar CI for National League games

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

**American:**

11.1, 10.8, 10.8, 10.3, 10.3, 10.1,10.0, 9.5, 9.4, 9.3, 9.2, 9.2, 9.0, 8.3

**National:**

14.0, 11.6, 10.4, 10.3, 10.2, 9.5, 9.5, 9.5, 9.5, 9.1, 8.8, 8.4, 8.3, 8.2, 8.1, 7.9

Kindly view attached picture for boxplot :

Using the relation :

Mean ± Zcritical * s/sqrt(n)

Zcritical at 95% = 1.96

National league :

Mean = 9.58125

Standard deviation = 1.5

9.58125 - 1.96 * 1.5/4 = 8.84625

9.58125 + 1.96 * 1.5/4 = 10.31625

(8.84625 ; 10.31625)

American League :

Mean = 9.807

Standard deviation = 0.805

9.807 - 1.96 * 0.805/sqrt(14)= 9.3853152

9.807 + 1.96 * 0.805/sqrt(14) = 10.228684

(8.84625 ; 10.31625)