Question

Monogram Masters states on its website that 92% of its orders
are ready to ship within five working days. A simple random sample
of 200 of the 3,000 orders received during the past month are
pulled for an audit. The audit shows that 175 of these orders were
shipped on time.

**Part A:** If Monogram Masters really ships 92% of
its orders within five working days, what is the probability that
the proportion in the simple random sample of 200 orders is as
small as the proportion in the auditors' sample or smaller?

**Part B:** A customer says, "Monogram Masters claims
92% of its orders are shipped on time, but its sample proportion is
less than that." Explain why the probability calculation shows the
result of the sample agrees with the 92% claim.

Answer #1

**Part A:** The hypothesized value of proportion is
So for sample
size the standard
deviation of distribution is

For given observation, the sample proportion

So the test statistic is

Required probability =

So the probability that proportion in the simple random sample of 200 orders is as small as the proportion in the auditors' sample or smaller is just less than 1%

**Part B:** It is 99% probable that the proportion
is not 0.92. Hence, there is enough evidence, at the 0.01 level,
that Monogram Masters ships less than 92% of its orders on time

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