Page 67 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing
11. An exit poll by a news station of 800 people in a certain parliamentary constituency finds 390 voting for
candidate A. Does the data support the hypothesis that candidate A receives 50% of the parliamentary
constituency’s votes at a significance level of 10%.

12. According to an article published 2 years ago, the mean number of cigarettes smoked per day by adults
who were daily smokers was 11.6. To determine whether adults who are daily smokers nowadays smoke
less than the general population of daily smokers in the past, a random sample of 100 adults who are
current daily smokers and record the number of cigarettes smoked on a randomly selected day. The
data give a sample mean of 10.8 cigarettes and a standard deviation of 3.9 cigarettes. Perform, at the
5% significance level, a test to determine whether current adults who are daily smokers smoke less
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than the general population of daily smokers two years ago.
13. A pizza shop in a district advertises that their average delivery time to the district is at most 15 minutes.
A sample of 60 delivery times has an average of 18 minutes. The true standard deviation of delivery
times is 8 minutes. Is there sufficient evidence to reject the shop’s claim at the 5% significance level?
14. For 150 bottles labelled as “350-millilitre”, the average amount of soft drink filled by the machine is
348.5 millilitres. The population standard deviation is known to be 11.5 millilitres. If the expected
amount (per bottle) of the soft drink filled by the machine is not equal to 350 millilitres, then the
machine is “out of control”, and must be shut down for repairs. Test whether the machine is out of
control at the 5% significance level.

15. A certain type of medicine is known to be 60% effective in relieving an arthritis pain. To determine
whether a new and somewhat more expensive patent medicine is superior in alleviating the arthritis
pain, a sample of 500 patients is taken and it is found that the new medicine provides relief of 318
patients. Carry out a test at a significance level of 5%.

16. The hourly french fried potato output by a certain brand fry machine is advertised to be 60 kilograms.
For the new machine purchased by a fast food restaurant, tests are run for 50 different one-hour periods,
producing an average output of 57.2 kilograms, with a standard deviation of 6.8 kilograms. At the 5%
level of significance, does the fast food restaurant management have grounds for complaints?
17. A random sample of 80 observations obtained from a population produces the results:
80 80
2
∑ x i = 2880, ∑ x i = 129 276.
i = 1 i = 1
(a) Calculate an unbiased estimate of the population mean and variance.
(b) Determine a 95% confidence interval for the population mean.
(c) Test, at the 5% significance level, H : μ = 34 against H : μ ≠ 34.
0
1
5 (d) Explain the relationship between the confidence interval obtained in (b) and the result of the test
in (c).
18. The mean lifetime of a sample of 200 picture tubes produced by a manufacturer is found to be
14 800 hours with a standard deviation of 1060 hours. Use a significance level of 5% to test, on the
basis of this data, whether the mean lifetime of all such tubes made is 15 000 hours as claimed by
the manufacturer.
19. In a sequence of rolling a dice 500 times, ‘ones’ are obtained 77 times. Test, at a significance level of
10%, the hypothesis that the dice is unbiased.
20. A traffic authority is concerned with the increasing traffic congestion in a city. The authority knows
that the mean time per journey between the city centre and the nearby town during the peak hours
was 32.5 minutes with a standard deviation of 19.7 minutes five years ago. This year, for a random
sample of 150 car drivers, the mean travelling time is 36.8 minutes. Does the authority justify the
worry about the traffic congestion getting worst this year if a significance level is chosen to be 5%?

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05 STPM Math(T) T3.indd 258 28/10/2021 10:24 AM