A catalog sales company promises to deliver orders placed on the Internet within
ID: 3055852 • Letter: A
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%.
(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.
Use the above information to answer Q1 and Q2.
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Q1. 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 %.
Q2. 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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