Question

Is the confidence interval appropriate?

• Independence Condition: Required. Guaranteed if the sample was random. If not, we have to consider whether it there’s any reason to suspect that individual outcomes could influence one another, or if there’s any reason to think the sample might not be representative.

• Randomization Condition: Optional. Met when the sample was randomly chosen. If met, guarantees the Independence Condition is met. This is also the best way to ensure a representative sample.

• < 10% Condition: Required. For the methods in this chapter, we need the sample size to be less than 10% of the population. Otherwise, different formulas/calculator functions are needed.

• Success/Failure Condition: Required. Whenever we are using the normal distribution with proportions, we must meet the “at least 10 successes” and “at least 10 failures” conditions. If the numbers are given as integers, we can just compare. If not, we calculate and check that ≥ 10 and 1 − ≥ 10.

6. For each scenario, indicate if the chapter 13 confidence interval is appropriate, and briefly explain why. (a) A prison has records on all 385 of its inmates and finds that 59% have been vaccinated against pararibulitis. (b) A random sample of 1178 inmates in prisons across Oklahoma finds that 59% have been vaccinated against pararibulitis. (Note: Oklahoma has more than 62,000 inmates) (c) A prison doctor notes that of the last 86 inmates to receive medical care, 59% have been vaccinated against pararibulitis.

Answer 1