12. The NYS transit authority is interested in the construction of a cross-sound bridge to connect Long Island directly to Connecticut. Since she's been in hot water recently and fears her re-election prospects dwindling. Governor Hochul doesn't want to move forward with the project unless it has the support of the majority of Long Islanders (i.e. more than 50%). She orders a poll conducted to assess public interest in the project. They survey a SRS of 1225 Long Island residents and find 621 of them support the bridge project.

(a) Is there convincing statistical evidence (at the significance level of a = 0.05) that the Governor should move forward with the project? Complete the appropriate inference procedure to support your answer.

(b) Based on your conclusion to part (a), which of the two errors (Type I or Type II could have been made?

Interpret a potential consequence of this error in context.