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 522 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. (Use a table or technology.)

Statement 1: It is unlikely that the estimate p = 0.87 differs from the value of the actual population proportion by more than 0.014.

a. Correct.

b. Incorrect, because the value 0.014 is the standard error of P rather than the margin of error. Incorrect, because it is unlikely that the estimate differs from the actual population proportion by less than 0.014, rather than by more than 0.014.

c. Incorrect, because the value 0.014 is the margin of error of Ộ rather than the standard error.

Statement 2: It is unlikely that the estimate p = 0.87 differs from the value of the actual population proportion by more than 0.027.

a. Correct.

b. Incorrect, because the value 0.027 is the standard error of p rather than the margin of error.

c. Incorrect, because it is unlikely that the estimate differs from the actual population proportion by less than 0.027, rather than by more than 0.027.

d. Incorrect, because the value 0.027 is the margin of error of rather than the standard error.

Statement 3: The estimate p = 0.87 will never differ from the value of the actual population proportion by more than 0.027.

a. Correct.

b. Incorrect, because in 5% of all possible random samples, the estimate will differ from the actual population proportion by more than 0.027.

c. Incorrect, because the estimate will never differ from the actual population proportion by less than 0.027.

d. Incorrect, because in 95% of all possible random samples, the estimate will differ from the actual population proportion by more than 0.027.