Discuss the below:
Assume that μ = 500 and σ = 100 for the GRE
Let's say there is a local company (rhymes with "Zaplan") that promises a score of 625-good enough for admission to your favorite graduate school-if you take their $1200 preparatory course.
Q1. Treat yourself as a sample of 1 (N=1). Is a score of 625 significantly higher than average? Is it worth $800? Explain how you use a statistical test to answer this question.
Q2. Assume you did not take the course. Your results have arrived in the mail, and you scored in the 90th percentile of the distribution (Hint: 10 of the population scored higher than you). Sound good? What was your score? Would you have done better if you had taken the preparatory course and scored the promised 625?
Q3. If 4 students took the preparatory course and their mean score is 625, have they scored significantly higher than average? Again, how does statistical reasoning help you to answer the question?
Q4. For the 4 students in the problem above, "figure" a 95% Confidence Interval around the sample mean.
Q5. Now, "figure" a 99% Confidence Interval around the sample mean. Look at the intervals for these two problems, and tell me why you can reject the Null Hypothesis in this problem with α = .05 but NOT with α = .01.