Is the probability of a bowler rolling a strike higher after he has thrown four consecutive strikes? An investigation into the phenomenon of a "hot hand" in bowling was published in The American Statistician (Feb. 2004). Frame-by-frame results were collected on 43 professional bowlers from the 2002-2003 Professional Bowlers Association (PBA) season. For each bowler, the researchers calculated the proportion of strikes rolled after bowling four consecutive strikes and the proportion after bowling four consecutive nonstrikes. The data on 4 of the 43 bowlers, saved in the HOTBOWLER file, are shown in the following table

a. Do the data on the sample of four bowlers provide support for the "hot hand" theory in bowling? Explain.
b. When the data on all 43 bowlers are used, the p -value for the hypothesis test is approximately 0. Interpret this result.

Proportion of Strikes After Four Strikes After Four Nonstrikes Bowler Paul Fleming Bryon Smith Mike De Vaney Dave D'Entremont 683 684 632 610 .432 400 421 .529