Question

A catalog sales company promises to deliver orders placed on the Internet within 3 days. ​ Follow-up calls to a few randomly selected customers show that a 90​% confidence interval for the proportion of all orders that arrive on time is 85​% ± 5​%. What does this​ mean? Are the conclusions below​ correct? Explain.

1. Between 80​% and 90​% of all orders arrive on time.
2. 90​% of all random samples of customers will show that 85​% of orders arrive on time.
3. 90​% of all random samples of customers will show that 80​% to 90​% of orders arrive on time.
4. The company is 90​% sure that between 80​% and 90​% of the orders placed by the customers in this sample arrived on time.
5. On 90​% of the​ days, between 80​% and 90​% of the orders will arrive on time

a) Choose the correct answer below.

A) This statement is correct.

B) This statement is not correct. It implies certainty.

C) This statement is not correct. No more than 90​% of all orders arrive on time.

D) This statement is not correct. At least 80​% of all orders arrive on time.

​b) Choose the correct answer below.

A) This statement is correct.

B) This statement is not correct. All random samples of customers will show that 85​% of orders arrive on time.

C) This statement is not correct. Different samples will give different results. 90​% of all random samples of customers will show that 80​% to 90​% of orders arrive on time.

D) This statement is not correct. Different samples will give different results. Most​ likely, none of the samples will have exactly 85​% ​on-time orders.

​c) Choose the correct answer below.

A) This statement is correct.

B) This statement is not correct. A confidence interval says something about the unknown population​ proportion, not the sample proportion in different samples.

C) This statement is not correct. All random samples of customers will show that 80​% to 90​% of orders arrive on time.

D) This statement is not correct. 90​% of all random samples of customers will show that 85​% of orders arrive on time.

​d) Choose the correct answer below.

A) This statement is correct.

B) This statement is not correct. The company is 90​% sure that 85​% of the orders placed by the customers in this sample arrived on time.

C) This statement is not correct. In this​ sample, it is known that 85​% arrived on time.

D) This statement is not correct. The company is 90​% sure that between 80​% and 90​% of the orders placed by the customers in all samples will arrive on time.

​e) Choose the correct answer below.

1. This statement is correct
2. This statement is not correct. Everyday between 80% and 90% of the orders will arrive on time.
3. This statement is not correct. On 90% of the days, 85% of the orders will arrive on time.
4. This statement is not correct. The interval is about the parameter, not about the days

Answer 1