The following data shows the number of hits and the number of at bats for 7 major league players in recent World Series. If there is enough evidence to suggest a strong linear relationship between at bats and hits, with a significance of 0.05, then predict the number of hits expected if a player gets 80 at bats. 

At Bats	51	67	77	44	55	39	45
Hits	19	25	30	20	23	16	18

Step 1:

Enter Data into calculator

We see that we have a p-value of 0.9999, this is greater that \(1-\frac{\alpha}{2}\) thus we reject the null hypothesis of \(\rho=0\) and hence we conclude that this sample suggests that it is likely that this data is linearly correlated.

Step 2:

Since we concluded that this data is linearly correlated we look back at our calculator and see that

\[a=3.2\]

\[b=0.34\]

So this means that we can approximate our data with the line

\[y=0.34x+3.2\]

Step 4:

To approximate the number of hits likely if a player gets 80 at bats, we replace the \(x\) in the above equation to get

\[\text{number of hits }=y=0.34\cdot(80)+3.2=30.4\]

So we should expect around 30.4 hits if we give a player 80 at bats.