In a sample of 800 people, 420 are in favor of a proposed scoring system. A golf course wants to implement an electronic scoring system where shots are counted by satellites to reduce human error and to show real-time scores at the clubhouse. Is there enough evidence to conclude that the majority of the golfing community is a proponent of the new system at an alpha level of .05. Determine the number of tails for this problem, the critical value and the test statistic.

There are two major tests of readiness for college: the act and the sat. act scores are reported on a scale from 1 to 36. the distribution of act scores in recent years has been roughly normal with mean µ = 20.9 and standard deviation s = 4.8. sat scores are reported on a scale from 400 to 1600. sat scores have been roughly normal with mean µ = 1026 and standard deviation s = 209. reports on a student's act or sat usually give the percentile as well as the actual score. the percentile is just the cumulative proportion stated as a percent: the percent of all scores that were lower than this one. tanya scores 1260 on the sat. what is her percentile (± 1)?