A large online retailer is interested in learning about the proportion of customers making a purchase during a particular month who were satisfied with the online ordering process. A random sample of 600 of these customers included 492 who indicated they were satisfied. For each of the three following statements, indicate if the statement is correct or incorrect. If the statement is incorrect, explain what makes it incorrect.
Statement 1: It is unlikely that the estimate ˆ p = 0.82 differs from the value of the actual population pro-portion by more than 0.0157.
Statement 2: It is unlikely that the estimate ˆ p = 0.82 differs from the value of the actual population pro-portion by more than 0.0307.
Statement 3: The estimate ˆ p = 0.82 will never differ from the value of the actual population proportion by more than 0.0307.