A reader wrote in to the \"Ask Marilyn\" column in Parade magazine to say that his grandfather told him that in three-quarters of all baseball games, the winning team scores more runs in one inning than the losing team scores in the entire game. (This phenomenon is known as a \"big bang\") Statistician Hal Stern (who just finished being Dean of the School of ICS here at UCI) examined all 968 baseball games played in the National league in 1986 and found that 419 of them contained a big bang. a) Perform the appropriate test to see whether or not this sample proportion differs signicantly from 0.5 at the a = 0.02 level. Make sure to clearly label your steps! Report your hypotheses in symbols and in words, your well-labeled sketch of the sampling distribution under the null hypothesis, your check of the technical conditions, the test statistic, and the pvalue, in addition to stating and explaining your conclusion. b) If you redene big bang to mean that the winning team scores at least as many (instead of more) runs in one inning as the losing team scores in the entire game, then 651 of those 968 games contained a big bang. Does this sample proportion differ signicantly from the \"Ask Marilyn\" reader's grandfather's assertion of 0.75 at the a = 0.08 level? Again report the details of your analysis