Suppose a principal at a school claims that their students are of above average intelligence compared to the general population of students in the province. To test their hypothesis, the principal randomly samples 47 students from their school and administers the SMART Exam, which ranges in scores from 0 to 80. In his sample he observed a mean score of 61. Historically, the average score for students on the SMART Exam has been a 54, with a standard deviation of 18.5. Is there sufficient statistical evidence to support the principal's claimif a=.01?(10points)

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State the population distribution(s) State the appropriate statistical hypotheses State the assumption(s) of the test Identify the test statistic and deduce the appropriate null distribution (i.e., if-then link) Specify alpha, set up null distribution, and choose a decision rule Run the test and make a decision Provide a brief APA-style write up of the statistical test that includes all relevant additional .

test estimates