Page 66 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 5 Hypothesis Testing

STPM PRACTICE 5

1. A random sample of 70 observations taken from a normal distributed population, with standard
–
deviation s = 7.2, gives the sample mean x = 60.8. Test, at the 5% significance level, H : μ = 60 against
0
H : μ . 60.
1
2. A random sample of 103 observations is taken from a certain population. It is found that its sample
mean is 189 with a standard deviation of 29.7. The null hypothesis H : μ = 200 is to be tested against
0
Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
H : μ ≠ 200. If the test is performed at the 2% significance level, what conclusion do you draw?
1
3. Suppose a random sample of 20 independent observations is obtained from a binomial distributed
population and the number of successes is 8. Use a significance level of 1% to test H : p = 0.20 against
0
H : p ≠ 0.20.
1
4. It is given that the number of successes, x = 85 and the number of independent observations,
n = 300 for a random sample obtained from a binomial distributed population. Use a significance
level, a = 0.05 to perform the hypothesis test H : p = 0.32 versus H : μ , 0.32.
1
0
5. A person claims that the weather forecasts by a meteorologist are no better than the outcomes of tossing
a fair coin. If a head is obtained then there will be no rain, and if a tail is obtained then there will be
rain. He records the weather for 50 randomly chosen days. The meteorologist forecast is correct on
34 of these days.
(a) Write the hypotheses clearly.
(b) Use a significance level of 1% to test the claim of the person.

6. An environmental department wants to determine whether a cleanup project at a lake has been effective.
This is to be done by recording dissolved oxygen content (in ppm, parts per million) in the lake, with
higher values indicating less pollution. Prior to the cleanup project the mean dissolved oxygen readings
around the lake is reported as 9.80. Six months after the initiation of the cleanup, a random sample
of 80 readings gives the mean and standard deviation as 9.95 ppm and 0.51 ppm respectively.
(a) State null and alternative hypotheses for a hypothesis test.
(b) Carry out the test at a significance level of 5%.
7. A shopkeeper realises that 20% of customers buy a drink from the storage. During the renovation of
the shop a new storage was installed. He picks a random sample of 20 customers and finds that only
1 customer have bought drinks from the new storage. Using a significance level of 5% to test whether
there has been a change in the proportion of customers buying a drink from the storage.
5
8. A real estate agent claims that 60% of all apartments being built today are 3-bedroom units. To test
this claim, a sample of 50 new apartments is inspected and it is found that the proportion of these
apartments with 3-bedroom units is 75%. Perform a hypothesis test at a significance level of 2%.
9. The contents of a random sample of 9 containers of a particular paint are 5.2, 4.7, 4.6, 5.3, 5.1, 4.8,
4.9, 5.4, and 4.8 litres. Assume that the contents is normally distributed with standard deviation 0.2
litre. Use a 10% significance level to determine whether the mean content of the containers is 5 litres.

10. The mean height of male students in a certain college has been 164.9 centimetres with a standard
deviation of 14.3 centimetres. Is there strong reason to believe that there has been a change in the mean
height of male students if a random sample of 90 male students in the college has a mean height of
168.5 centimetres? Assume that the sample standard deviation remains the same and use a significance
level of 5%.

257

05 STPM Math(T) T3.indd 257 28/10/2021 10:24 AM