Question

Judging by the $F$ statistic, do you think it is likely or unlikely that you will reject the null hypothesis?

Short answer

The null hypothesis of no difference between the means of goals in four different score teams will be rejected, because the $P$-value $0.00048$ is less than the level of significance $0.05$.

Step-by-step solution

Given Information

Girls from four different soccer teams are to be tested for mean goals scored per game. The entries in the table are the goals per game for the different teams.

Team 1	Team 2	Team 3	Team 4
1	2	0	3
2	3	0	4
0	2	1	4
3	4	1	3
2	4	0	2

Explanation

Consider the null hypothesis that there is no difference between the means of goals in four different score teams.

Use Ti-83 calculator for calculation. For this, click on STAT $\to$press $1\to$EDIT, then put the above given weights of different groups data into the list $L1,L2,L3andL4$. The screenshot is given as below:

Explanation

Now again press STAT $\to$arrow over the TESTS $\to$arrow down to ANOVA $\to$Press var then select $1$, press var then select $2$, press var then select $3$and press var then select $4$to fill the values of $L1,L2,L3andL4$. The screen shot is given as below:

Explanation

Press ENTER. The screenshot of the obtained output is given as below:

Thus, value of $F$-Statistic is $10.40$and the corresponding $p$-value is $0.00048$. Thus at $5\%$level of significance, the null hypothesis of no difference between the means of goals in four different score teams will be rejected, because the $P-$value $0.00048$is less than the level of significance $0.05$.