A catalog sales company promises to deliver orders placed on the Internet within

Question

A catalog sales company promises to deliver orders placed on the Internet within three days. Follow-up calls to randomly selected customers show that a 95% confidence interval for the proportion of all orders that arrive on time is 90% ±7%.

What does this mean? Are the following conclusions correct?

(a) Between 83% and 97% of all orders arrive on time.

(b) 95% of all random samples of customers show that 90% of orders arrived on time.

(c) 95% of all random samples of customers will show that 83% to 97% of orders arrived on time.

(d) We are 95% sure that between 83% and 97% of the orders placed by the customers in this sample arrived on time.

(e) On a randomly chosen day, we can be 95% confident that between 83% and 97% of the large volume of orders will arrive on time.

What does this mean?

A. This means that there is a 95% chance that the standard deviation is 77%.

B. This means the procedure that produced this interval generates ranges that hold the population mean for 95% of samples.

C. This means that we are 95% sure that all orders arrive on time.

D. This means that there is a 95% chance that the mean proportion is 90 %.

Are the conclusions given in the problem statement correct? Select all that apply.

(a)

(b)

(c)

(d)

(e)

None of the above

Explanation / Answer

a) Not correct. This implies certainty.

b) Not correct. Different samples will give different results.

Many fewer than 95% will have 90% on-time orders.

c) Not correct. The interval is about the population proportion, not the sample proportion in different samples.

d) Not correct. In this sample, we know 90% arrived on time.

e) Not correct. The interval is about the parameter, not about the days.

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