A car manufacturer is interested in learning about the proportion of people purchasing one of its cars who plan to purchase another car of this brand in the future. A random sample of 400 of these people included 267 who said they would purchase this brand again. For each of the three statements below, indicate if the statement is correct or incorrect. If the statement is incorrect, explain what makes it incorrect.
Statement 1: The estimate ˆ p = 0.668 will never differ from the value of the actual population proportion by more than 0.0462.
Statement 2: It is unlikely that the estimate ˆ p = 0.668 differs from the value of the actual population pro-portion by more than 0.0235.
Statement 3: It is unlikely that the estimate ˆ p = 0.668 differs from the value of the actual population pro-portion by more than 0.0462.