Question

Monogram Masters advertises on its website that 92% of customer orders are received within five working days. They performed an audit from a random sample of 200 of the 3,000 orders that month and it shows 175 orders were received on time.

Part A: Can we use a normal approximation? Explain. (5 points)

Part B: If Monogram Masters customers really receive 92% of its orders within five working days, what is the probability that the proportion in the random sample of 200 orders is the same as the proportion found in the audit sample or less? (5 points)

Answer 1

We are given Sample proportion p=0.92

p=0.92, q=1-p=1-0.92=0.08, n=200

So the test statistic

Required probability = P(Z< -2.34)=0.0096 [ Using Excel command =normsdist(-2.34)]

Therefore, the probability that in the simple random sample of 200 orders, is as small as the proportion in the auditor’s sample or smaller is just less than 1%

b) It is 99% probable that the proportion is not 0.92. There is enough evidence at the 0.01 level of significance that Monogram Masters ship less than 92% of its orders on time.

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