Page 58 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing
6. An electrical company manufactures light bulbs, their life times measured in hours, approximately
normally distributed. The company claims that the light bulb has a mean life time of 1000 hours with
a standard deviation of 86 hours. A customer suspects that the mean life time may be lower. He tests
a random sample of 35 light bulbs and finds that the average life time is 960 hours. At the significance
level of 5%, does the data provide evidence to conclude that mean life time of a light bulb is 1000
hours claimed by the company?
7. A manufacturer claims that the mean fat content of his hot dog is 10%. Assume that percentage fat
content to be normally distributed with standard deviation of 3%. A consumer group, concerned about
the fat content of hot dog, submits a random sample of 30 hot dogs to a laboratory for analysis. The
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laboratory result shows that the mean fat content of the hot dog is 12%. Carry out an appropriate
hypothesis test, using significance level of 1%, in order to advise the consumer group as to the validity
of the manufacturer’s claim.
8. 9 babies are born in a hospital in a particular day. The weights, in kg, of the babies are recorded as
follows:
2.9 3.2 3.0 2.8 3.4 2.7 3.1 3.0 2.8
Assume that the sample is from a normally distributed population with standard deviation 0.3 kg.
Carry out a test, at the 5% significance level, on the hypothesis that the population mean weight is 3
kg.
9. A car manufacturer advertises a car that has 20 km/l fuel consumption. A random sample of 30 cars
gives a mean petrol mileage of 18.7 km/l with standard deviation 3.81 km/l. Assume that the sample
is from a normal population. Test the manufacturer’s claim at the 5% significance level.
10. The random variable X has a normal distribution with standard deviation σ = 21. A random sample of
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size 16 gives the sample mean x = 89. Determine a 90% confidence interval for the population mean.
Then, test H : μ = 95 against H : μ ≠ 95 using a = 0.1. Explain how this confidence interval can be
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used to test the hypothesis.
11. Production records show that a machine makes coins with a mean diameter of 24.5 mm. An inspector
selects a random sample of 100 coins and obtains a mean diameter of 25.3 mm with a standard deviation
of 2.57 mm. Determine whether the machine slipped out of normal operation at the 1% significance
level?

12. The national mean cholesterol level is approximately 220 units. 50 patients with high cholesterol levels
(over 265) participate in a drug study and are treated with a new drug. After treatment the sample
mean is 235 and the sample standard deviation is 41. One question of interest is whether people taking
this new drug still have a mean cholesterol level that exceeds the national average. What conclusion
would you get from this study by using a significance level of 2%? 5
13. A random sample of 40 steel bars is taken from one of the production lines. It is found that the sample
mean and sample standard deviation are 28 kg and 4.5 kg respectively. Investigate the claim that the
mean mass of a steel bar is 30 kg. Use a significance level of 5%.
14. It is claimed that a car owner drives, on average, more than 25 000 km per year. To test this claim,
a random sample of 60 car owners are asked to keep a record of the distance they travel. Would you
agree with this claim if the random sample shows an average of 26 500 km and a standard deviation
of 7590 km? Use a significance level of 5%.
15. A production supervisor measures the filled volume of a random sample of 80 cans of mango
juice labelled as containing 350 ml. The sample has mean volume 348.2 ml and standard deviation
5.9 ml. Let μ represent the mean volume for all cans of mango juice recently filled by this machine.
The supervisor test H : μ = 350 against H : μ ≠ 350 at a significance level of 1%.
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(a) Find the critical values in ml.
(b) Explain whether the mean filled volume differs from 350 ml?

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05 STPM Math(T) T3.indd 249 28/10/2021 10:24 AM