Question

Lotteries and contests in Canada are required by law to state the odds of winning. For example, the BC Lotto Max main jackpot has a 1 in 33.3 million (so p ≈ 3 · 10−8 ). Suppose we didn’t know the population proportion of jackpot winners, and wanted to calculate it using a sample of 1000 lottery players. (A) Explain why the techniques we used in class are not appropriate for finding a confidence interval for the proportion of jackpot winners. (B) Suppose our sample of 1000 lottery players contained zero winners. Even though we shouldn’t, use the techniques in class to find a 99% confidence interval. (C) Suppose our sample of 1000 lottery players contained one winner. Even though we shouldn’t, use the techniques in class to find a 99% confidence interval. (D) Explain why your answers to part (B) and (C) support the fact that we should not use the techniques from class to find a confidence interval. In other words, explain the problems with the confidence intervals found in parts (B) and (C).

Answer 1

And as we know that there should be approximately 1 success in 33.3 million people, so this confidence interval gives misleading information.

Hence, we can't use the technique taught in class to calculate such intervals.