The first day of baseball comes in late March, ending in October with the World Series. Does fan support grow as the season goes on? Two CNN/USA Today/Gallup polls, one conducted in March and one in November, both involved random samples of 1001 adults aged 18 and older. In the March sample, 45% of the adults claimed to be fans of professional baseball, while 51% of the adults in the November sample claimed to be fans.
a. Construct a 99% confidence interval for the difference in the proportion of adults who claim to be fans in March versus November.
b. Does the data indicate that the proportion of adults who claim to be fans increases in November, around the time of the World Series? Explain.