Your mail order company advertises that it ships 90% of its orders
within three working days. You select an SRS of 100 of the 5000 orders
received in the past week for an audit. The audit reveals that 86 of
these orders received in the past week for an audit. The audit reveals
that 86 of these orders were shipped on time.
a) What is the sample proportion of orders shipped on time?
b) If the company really ships 90% of its orders on time, what is the
probability that the proportion in an SRS of 100 orders is as small as
the proportion in your sample or smaller?
c) A critic says, "Aha! You claim 90%, but in your sample the on-time
percentage is lower than that. So the 90% claim is wrong." Explain in
simple language why your probability calculation in (b) shows that the
result of the sample does not refuge the 90% claim.
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