Page 52 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing
6. There are two wrong conclusions from which you could draw in a hypothesis test: Type I and Type
II errors. Identify the Greek letter to denote the probability of each type of error.
7. The null hypothesis H : p = 0.35 is tested against the alternative hypothesis H : p . 0.35, where p is
0
1
a population proportion.
(a) Suppose that the decision procedure leading to nonrejection of the null hypothesis when in fact
it is false. What type of error is committed?
(b) If the decision procedure leading to the rejection of the null hypothesis when in fact it is true.
What type of error is committed?
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8. Consider the null hypothesis, H : A new teaching technique and the conventional classroom procedure
0
are equally effective versus the alternative hypothesis, H : A new teaching technique is either inferior
1
or superior to the conventional procedure. Describe the decisions taken that would result in Type I
and Type II errors if H is tested.
0
9. For the following statements, what happens to the likelihood that we reject the null hypothesis?
(a) The closer the value of a sample mean is to the value stated by the null hypothesis.
(b) The further the value of a sample mean is from the value stated in the null hypothesis.
10. Suppose one reads news stating that children in his country watch, on average, 5 hours of television
per week. In order to test this claim, he conducts a study on a random group of 30 children and finds
that the children in the group spend, on average, 4.6 hours watching television per week.
(a) State the null and alternative hypotheses.
(b) If the decision “reject the null hypothesis” is adopted, what decision error could be committed?
(c) Assume the decision “fail to reject the null hypothesis” is implemented, what decision error could
be made?
(d) State whether the test is a one-tailed test or a two-tailed test.

11. The normal curve for testing a null hypothesis H : µ = 50 is shown below.
0

0.025 0.025
–
x
25  = 50 75
Determine the
(a) rejection region, 5
(b) nonrejection region,
(c) critical values,
(d) significance level.

12. The normal curve for testing a null hypothesis H : µ = 32 is shown below.
0

0.01
–
x
31  = 32

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05 STPM Math(T) T3.indd 243 28/10/2021 10:24 AM