The principal collects information on the annual family income for every single student who attends Brickell High School. The annual family income for all students who attend Brickell High School is $52,116, with a standard deviation of $10,701. Every year, 9 students are elected by their peers to serve on the Student Council for Brickell High School. However, the principal is concerned that these 9 students elected for Student Council might have a higher annual family income than most students at Brickell High School, and therefore, might not be a representative sample of the student body. The average annual family income for these 9 students is $54,827. Is the average annual family income of the students on Student Council at Brickell High School significantly different from the average annual family income of all students at Brickell High School? Use a nondirectional alternative hypothesis and α = 0.01 to analyze this data. Answer all of the following questions. Please label each step with the appropriate letter. A. Identify the two hypotheses. B. Determine the critical region for your decision. C. Compute the test statistic. D. Use the test statistic to make a decision and interpret that decision.
The principal collects information on the annual family income for every single student who attends Brickell High School. The annual family income for all students who attend Brickell High School is $52,116, with a standard deviation of $10,701. Every year, 9 students are elected by their peers to serve on the Student Council for Brickell High School. However, the principal is concerned that these 9 students elected for Student Council might have a higher annual family income than most students at Brickell High School, and therefore, might not be a representative sample of the student body. The average annual family income for these 9 students is $54,827. Is the average annual family income of the students on Student Council at Brickell High School significantly different from the average annual family income of all students at Brickell High School? Use a nondirectional alternative hypothesis and α = 0.01 to analyze this data. Answer all of the following questions. Please label each step with the appropriate letter.
A. Identify the two hypotheses.
B. Determine the critical region for your decision.
C. Compute the test statistic.
D. Use the test statistic to make a decision and interpret that decision.
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