In 2016, the Better Business Bureau (BBB) settled 80% of complaints they received in the US. Suppose you have been hired by the BBB to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the BBB is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.8, the same as the overall proportion of complaints settled in 2016.
1. Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of p̄.
2. Based on a sample of 200 complaints, what is the probability that the sample proportion will be within 0.04 of the population proportion?
3. Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of p̄.
4. Based on the smaller sample of only 450 complaints, what is the probability that the sample proportion will be within 0.04 of the population proportion?
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