Question: Suppose you heard a report on TV that 50% of students in Midwest College fail their final exam in a mathematical course. You want to see whether the report is true. To investigate this, you take a random sample of 20 students in Midwest College that have taken the mathematical class and find that 6 of them (30%) failed their final exam. You conducted a test of significance using simulation and get the following null distribution . (Note this null distribution uses only 100 simulated samples and not the usual 1000 or 10,000.)

1. Using the null distribution above, what is the p-value when testing H ₀ : π = 0.5 versus an alternative of H _a : π < 0.5. ( 2 pts )
2. Using the null distribution above, what is the p-value when testing H ₀ : π = 0.5 versus an alternative of H _a : π ≠ 0.5. ( 2 pts )
3. Using the null distribution above, get simulated based standardized statistic (z). ( 2 pts )
4. Using the 2SD method, find a 95% confidence interval for the proportion of all students in Midwest College that failed the final exam in that mathematical course. ( 2 pts )

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