Question

The American League and the National League of Major League Baseball are each divided into three divisions: East, Central, and West. Many years, fans talk about some divisions being stronger (having better teams) than other divisions. This may have consequences for the postseason. For instance, in $2012$Tampa Bay won $90$games and did not play in the postseason, while Detroit won only $88$and did play in the postseason. This may have been an oddity, but is there good evidence that in the $2012$season, the American League divisions were significantly different in overall records? Use the following data to test whether the mean number of wins per team in the three American League divisions were the same or not. Note that the data are not balanced, as two divisions had five teams, while one had only four

Short answer

The $P$-value is localid="1649231558940" $0.25$and the null hypothesis will be rejected on the $5\%$level of significant and the mean value will be different in all three groups.

Step-by-step solution

Given information

Given in the question that tables that contains data.

Use Ti-83 calculator 

Here we are going to check the mean number of wins of the team in the American League division in the given data are the same or not.

To check we need to do the calculation in the Ti-83 calculator

For the calculation of the mean number follow the step.

Click on STA $\to$press $\to$EDIT, then put data into the list $L1,L2$, and $L3$. The screenshot is given below:

Again press STAT $\to$arrow over the TESTS $\to$arrow down to ANOVA $\to$Press var then select $1$, press var then select $2$, and press var then select $3$to fill the values of $L1,L2$, and $L3$. The screenshot is given below:

Calculate the value of p

The result obtained after the calculation is given below.

So, From the result the $P$-value is localid="1649231584219" $0.25$

Therefore at the $5\%$level of significance the null hypothesis will be rejected.

The mean of the three groups will be different