Let’s say a player typically gets a hit in 3 out of every 10 at-bats (for a 0.300 batting average). Suppose the player has not had a hit in his previous four at-bats. In baseball, you will often hear an announcer say, “This player is due for a hit.” What does the announcer mean by this? Is the announcer’s statement true? The announcer is saying that if a player gets a hit in 3 of every 10 at-bats and has not had a hit in his previous 4 at-bats, the nonexistent law of averages must apply. To see why the announcer’s statement is not true, use the data set 5_1_51 found at www.pearsonhighered.com/sullivanstats and answer the following questions. In the data, the first four columns contain a 0 or 1. If the entry is 0, then the player does not get a hit, and if the entry is 1, then the player gets a hit. Each row represents a sequence of four at-bats. For example, in row 4, the player got a hit in his first and third at-bat but did not get a hit in his second and fourth at-bat.
(a) What was the outcome of the player’s at-bats based on the entries in the first four columns of row 1? Row 5?
(b) Column 5 contains the number of hits in the player’s previous four at-bats. We are only interested in those entries where the player had 0 hits in his previous four at-bats. Column 6 indicates whether the player got a hit in the fifth at-bat. For example, in row 1, the player did not get a hit in at-bat 5, but the player did get a hit in at-bat 5 in row 2. Among those instances where the player did not get a hit in his first four at-bats, determine the proportion of times in at-bat 5 the player gets a hit. To do this in StatCrunch, select Stats 7 Tables 7 Frequency. Under Select columns choose AtBat5. Under Where enter “Hits Previous 4” = 0. Click Compute! What proportion of fifth at-bats results in a hit when the previous four at-bats did not result in a hit? What does this tell you?