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Worked solution

Turn three claims into hypotheses

Define the hypotheses H0H_0 and H1H_1 to test (a) a claim that a supermarket manager has overstated the mean time spent shopping by customers in his store as 25 minutes; (b) a claim that the mean cholesterol level of all Singaporeans as 190 has been understated; and (c) if the average height of a population is different from 168 cm.

CJC · Lecture · Self-Practice 1

(a) Overstated shopping time

Let μ\mu be the population mean shopping time in minutes. H0:μ=25H_0:\mu=25 and H1:μ<25H_1:\mu<25: an overstated value is above the actual mean.

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(b) Understated cholesterol level

Let μ\mu be the population mean cholesterol level. H0:μ=190H_0:\mu=190 and H1:μ>190H_1:\mu>190. The source gives no unit, so none is invented.

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(c) A different mean height

Let μ\mu be the population mean height in cm. H0:μ=168H_0:\mu=168 and H1:μ≠168H_1:\mu\ne168. “Different” allows a change in either direction.

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Common mistakes

Do not reverse the alternative: overstated means the true mean is lower; understated means it is higher.

Solution notes

Both copies leave all three answer boxes blank. These worked answers are independently authored, compared with the printed asks and the source hypothesis definitions. No printed marks or exam attribution.

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