The PG County conducts annual surveys with twenty-five randomly assigned members of the community to evaluate their perception of safety. If the person claims that the criminal activity has not changed when compared with last year his answer receives a score of one hundred. If the persons believes that it has increased x% his answer receives a score of one hundred plus x. If he thinks it has fallen by x% his answer receives a score of one hundred minus x. The surveys have been conducted for many years and the historical average is one hundred with a standard deviation of thirty points. This year two local parties have been eagerly debating whether crime rates have increased in 2010 in order to decide an increase in the size of the county's police force.
a. Both parties agree that if the average score in this year's survey is greater than one hundred and eight they will increase the police force. Is this decision rule adequate? What is the Type 1 error of this rule?
b. A student from the Econ 321 class advices them that in statistics it is common practice to cap the Type 1 error at five percent. If they wanted to change their rule to comply with the common practice, what should be their new decision rule to decide whether to increment the police force?