Page 64 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing
6. 15% of mothers in a country who gave birth last year were under 20 years of age. A sociologist claims
that births to mothers under 20 years of age is decreasing. He selects a random sample of 25 births
this year and finds that 2 of them are to mothers under 20 years of age. Use a significance level of 1%
to test the sociologist’s claim.

7. At a certain college, it is estimated that around 30% of the students drive cars to class. In a random
sample of 20 college students chosen, 7 are found to drive cars to class. Determine, at the 5% significance
level, whether the 30% of the students driving to college is a valid estimation.

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8. Suppose that there are 38 occurrence from a sample of 60 independent observations obtained from
a binomial distribution. Find the z-value of the test statistic for the hypotheses test of H : p = 0.5
0
against H : p ≠ 0.5.
1
9. Suppose that X = 8 is an observation obtained from a random sample of size n = 25. The sample is
drawn from a binomial distribution. Consider the following test of hypothesis:
H : p = 0.4
0
H : p , 0.4
1
Compute an exact probability, P(X < 8), and compare it with the corresponding probability using a
normal approximation.

10. A construction firm claims that the job of covering housing floors with tiles is 80% completed in a
new housing estate. Would you agree with this claim if a random survey of new houses in this estate
shows that 32 out of 50 have floor job completed? Use a significance level of 5%.

11. A sample survey indicates that, out of 650 births, 327 are boys and the rest are girls. Do these figures
confirm the hypothesis that the sex ratio is 50 to 50? Use a significance level of 10%.

12. A club claims that it receives 12% responses from its mailing to club members. A random sample of
200 shows that only 18 members respond. Test the claim at a significance level of 10%.

13. A study estimates that 47 per cent of people in a city wear spectacles. However, you believe the
proportion of people in the city who wear spectacles is less than 47 per cent. You conduct a study
and find that, among 250 randomly selected people in the city, 114 of them wear spectacles. Test, at
the 5% significance level, the estimation that 47 per cent of people in the city wear spectacles.

14. A patented medicine claims that it is effective in curing 80% of the patients suffering from cold. From
a sample of 100 patients using this medicine, it is found that only 72 are cured. Determine whether 5
the claim is valid at the 5% significance level.

15. In a controlled laboratory experiment, scientists discovers that 35% of a certain rats subjected to a
cancer-causing chemical injection later develop cancerous tumours. Would we have reason to believe
that the proportion of rats developing tumours when subjected to this injection has increased if a
repeated experiment finds that 26 of 60 rats develop tumours? Use the 5% level of significance.

16. A random sample of 120 recent donations at a certain blood bank reveals that 55 are of type O
blood. Does this suggest that the actual percentage of type O donations differs from 38%, the
percentage of the population having type O blood? Carry out an appropriate hypothesis test using
a significance level of 10%. Would your conclusions have been different if a significance level of 5%
had been used?

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05 STPM Math(T) T3.indd 255 28/10/2021 10:24 AM