Page 51 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing
The choice of a one-tailed or a two-tailed alternative hypothesis depends on the conclusion to be drawn
if H is rejected. The position of the critical region can only be finalised once H has been stated.
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For example, a manufacturer of electrical kettle conducts a test on the incoming heating element from
a supplier. He needs some criterion for deciding whether the average number of damaged elements has
increased, because he concerns about incurring an unnecessary financial loss. He sets up the hypothesis
that there is no change in damage rate and tests this against the alternative hypothesis that new shipment
received has higher defective rate. Such an alternative hypothesis will result in a one-tailed test with the
critical region located at the right tail.

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Example 4

A consumer group suspects that a local store’s 100 g packages of dried mangoes actually weigh less than
100 g. The group takes a random sample of 50 such packages and finds that the mean mass for the
sample is 99 g.
(a) State the null and alternative hypotheses for the hypothesis test.
(b) Determine whether hypothesis test is two-tailed test or one-tailed test and the location of the critical
region.

Solution: (a) H : µ = 100 g,
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H : µ , 100 g.
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(b) The group concerns only the mass of the packages less than 100 g and
thus test against the alternative hypothesis that the mass is inferior. Such
an alternative hypothesis will result in a one-tailed test with the critical
region falling in the extreme left tail of the distribution.

Exercise 5.1

1. A defendant who has been indicted for committing a crime stands trial in a court. Based on the
evidence, the judge will make a decision whether the defendant is innocent or guilty. State the null
and alternative hypotheses for the above court case.
2. A new drug is developed by a pharmaceutical company. It is the responsibility of the government to
5 judge the safety and effectiveness of this drug before allowing it to be sold to the public. State the null
and alternative hypotheses for this case.
3. A multiple-choice test consisting of 20 questions, each with five possible answers of which one is correct,
is given to a student. The purpose of this test is to determine the student’s familiarity with the subject.
A score of 8 or more correct answers will convince the examiner that the student has knowledge of
the subject being tested and is not simply guessing. Determine the null and alternative hypotheses for
setting up the hypothesis test.
4. A manufacturer of sports equipment has developed a new synthetic fishing line claimed to have a mean
breaking strength of 8 kg. If a random sample of 30 lines is tested and found to have a mean breaking
strength of 7.9 kg. Determine the null and alternative hypotheses for setting up the hypothesis test.
5. The recommended adequate intake of calcium for adults is 1000 mg per day. If we want to carry out a
hypothesis test whether the average adult on diet gets a daily intake of less than 1000 mg of calcium.
State the null and alternative hypotheses.

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05 STPM Math(T) T3.indd 242 28/10/2021 10:24 AM