Tutorial 4 Hypothesis Testing
SUBJECT: Applied Statistics
CODE : BCT 2053
-TUTORIAL 4CHAPTER 4
1. A survey claims that the average cost of a hotel room in Riau is RM69.21. In order to
see if this is correct, a researcher selects a sample of 30 hotel rooms and finds that the
average cost is RM68.43. The standard deviation of the population is RM3.72. At
  0.05 , is there enough evidence to reject the claim?
2. The average serum cholesterol level in a certain group of patients is 240 milligrams.
The standard deviation is 18 milligrams. A new medication is designed to lower the
cholesterol level if taken for one month. A sample of 40 people used the medication
for 30 days, after which their average cholesterol level was 229 milligrams. At
  0.01 , does the medication lower the cholesterol level of the patients?
3. A manufacturer states that the average lifetime of its television sets is more than 84
months. The standard deviation of the population is 10 months. One hundred sets are
randomly selected and tested. The average lifetime of the sample is 85.1 months. Test
the claim that the average lifetime of the sets is more than 84 months, and should the
null hypothesis be rejected at   0.01 ?
4. The average amount of rainfall during the summer months for the northeast part of
the United States is 11.52 inches. A researcher selects a random sample of 10 cities in
the northeast and finds that the average amount of rainfall for 1995 was 7.42 inches.
The standard deviation of the sample is 1.3 inches. At   0.05 , can it be concluded
that for 1995 the mean rainfall was below 11.52 inches?
5. An officer states that the average fine levied by the safety office against companies is
at most RM350. A company owner suspects it is higher. She samples 12 companies
and finds that the average is RM358. The standard deviation of the sample is RM16.
Test the claim that the average is higher than RM350, at   0.05 .
6. From past experience, a teacher believes that the average score on a Statistics exam is
75. A sample of 20 students’ exam scores is as follows:
80, 68, 72, 73, 76, 81, 71, 71, 65, 50,
63, 71, 70, 70, 76, 75, 69, 70, 72, 74
Can the teacher conclude that the students’ average is still 75? Use   0.01 .
7. A toy manufacturer claims that at least 23% of the 14 year old residents of a certain
city own a skateboard. A sample of forty 14 year olds shows that seven own a
skateboard. Is there enough evidence to support the manufacturer’s claim at
  0.05 ?
8. A telephone company wants to advertise that more than 30% of all its customers have
at least two telephones. To support this advertise, the company selects a sample of
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Tutorial 4 Hypothesis Testing
200 customers and finds that 72 have more than two telephones. Does the evidence
support the ad? Use   0.05
9. A publishing company wishes to test the claim that there is a difference between two
overnight delivery companies in the speed with which their material is delivered. The
average speed of material delivered over a 30 day period is shown here. At   0.01 ,
is there enough evidence to support the claim that there is a difference between the
delivery times of the two companies if the variances population are not same?
Company 1
X 1  16hours
Company 2
X 2  18hours
 1  3.2
2  3
n1  30
n2  30
10. A medical researcher wishes to see whether the pulse rates of smokers are higher than
the pulse rates of nonsmokers. Samples of 100 smokers and 100 nonsmokers are
selected. The results are shown here. Can the researcher conclude, at   0.05 , that
smokers have higher pulse rates than nonsmokers if the variances population are
different?
Smokers
Nonsmokers
X 1  90
X 2  88
s1  5
s2  6
n1  100
n2  100
11. A manufacturer assumed that the mean lifetime for a type of battery is 2000 hours.
Random samples of 200 batteries are tested and it shows that the mean lifetime is
1996 hours with standard deviation 25.5 hours. Can we accept his hypothesis at
significance level, α = 0.01?
12. A company having two types of machine which produces an electronic component.
The company assumed that the proportions of defect components produce by both
machines are same. Random samples are chosen for both machines and the
information presented below. Do the information provide sufficient evidence to
conclude that the proportions of defect components produce by both machines are
same at significance level, α = 0.05?
Machine
Sample size
Number of defect component
1
150
12
2
200
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13. A restaurant owner states that 80% of his customers like to eat ‘nasi ayam’ at his
restaurant at lunch hour. 78 from random samples of 100 customers said that they like
to eat ‘nasi ayam’. Can we accept his hypothesis at significance level, α = 0.05?
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14. A car manufacturer company wants to buy either type A tires or type B tires for its
new car model. A test is done using both tires and the result shows below.
Type A: x1  37900 km, s1  5100 km, n1  10 cars
Type B: x1  39800 km, s2  5900 km, n2  12 cars
At significance level, α = 0.05, test a hypothesis that there is no different between
both types of tires. Assume that the population is normally distributed and not equal.
15. A random sample of 36 types of drink water at a vending machine contains an
average of 21.9 deciliters with standard deviation 1.42 deciliter water in each tin. Test
a hypothesis that   22.2 deciliter versus an alternative hypothesis   22.2
deciliter at significance level, α = 0.05.
16. A Random sample of sizes 25 are chosen from a normal population with standard
deviation 5.2 and mean 81. The second random sample of sizes 6 are also chosen
from a normal population with standard deviation 3.4 and mean 76. Test a hypothesis
H o : 1   2 versus H1 : 1   2 at significance level, α = 0.06. Assume that  1   2
17. In a survey, 56 from 200 smokers love to buy type ‘A’ cigarette while 29 from 150
smokers love to buy type ‘B’ cigarette. Can we conclude that at significance level,
α = 0.05 the selling for type ‘A’ cigarette is higher than the selling for type ‘B’
cigarette.
18. A distributor declared that at least 95% of equipment provide by his company fulfill
the specification list. In an inspection, 200 samples of equipments are tested and 18 of
the samples are not fulfilling the specification list. Test his hypothesis at significance
level, α = 0.05 and α = 0.01.
19. Two methods used to purify a protein are being compared. In 50 runs of method A,
the mean recovery was 60% and the standard deviation was 15%, while in 60 runs of
method B, the mean recovery was 65% and the standard deviation was 20%. Can you
conclude that there is a difference in the two recovery rates at significance level
α = 0.05? Assume that  1   2
20. A bird shooter states that 80% of his shoots were exactly killed the birds. Do you
agree with his hypothesis if in a given day he only can perfectly shoots and killed 9
from 15 birds? Use significance level, α = 0.05.
21. Two methods have been developed to determine the nickel content of steel. In a
sample of five replications of the first method on a certain kind of steel, the average
measurement (in percent) was X  3.16 and the standard deviation was 0.042. The
average of seven replications of the second method was Y  3.16 and the standard
deviation was 0.048. Assume that it is known that the population variances are nearly
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Tutorial 4 Hypothesis Testing
equal. Can we conclude that there is a difference in the mean measurements between
the two methods at significance level α = 0.05 if the variance population are equal?
22. In a survey of 100 randomly chosen holders of certain credit card, 57 said that they
were aware that used of the credit card could earn them frequent flier miles on a
certain airline. After an advertising campaign to build awareness of this benefit, an
independent survey of 200 credit card holders was made, and 135 said that they were
aware of benefit. Can you conclude that awareness of benefit increased after the
advertising campaign? Given that α = 0.05.
23. Two samples with sizes 11 and 14 from two independent normal population have
mean and standard deviation x1  75, x2  60, s1  6.1, s2  5.3 .Test an hypothesis
H o : 1   2 versus H1 : 1   2 at significance level, α = 0.05. Assume that the
population is same.
24. A machine filles 12-ounce bottles with soda. For the machine to function properly,
the standard deviation of the sample must be less than or equal to 0.03 ounce. A
sample of eight bottles is selected, and the number of ounces of soda in each bottle is
given as follows: 12.03 12.10 12.02 11.98 12.00 12.05 11.97 11.99
At α = 0.05, can we reject the claim that the machine is functioning properly?
25. Listed below are waiting times (in minutes) of customers at a bank.
6.5
6.8
7.1
7.3
7.4
7.7
The management will open more teller windows if the standard deviation of waiting
times (in minutes) is exceed 0.9 minutes. Is there enough evidence to open more
teller windows at α = 0.01?
26. A broth used to manufacture a pharmaceutical product has its sugar content, in
mg/mL, measured several times on each of three successive days.
Day 1:
5.0
4.8
5.1
5.1
4.8
5.1
4.8
4.8
5.0
5.2
4.9
4.9
5.0
Day 2:
5.8
4.7
4.7
4.9
5.1
4.9
5.4
5.3
5.3
4.8
5.7
5.1
5.7
Day 3:
6.3
4.7
5.1
5.9
5.1
5.9
4.7
6.0
5.3
4.9
5.7
5.3
5.6
a. Can you conclude that the variability of the process is greater on the second day
than on the first day?
b. Can you conclude that the variability of the process is greater on the third day
than on the second day?
Given that α = 0.05.
27. A researcher wants to see if a method (Method 1) for measuring the arsenic
concentration in soil is significantly more precise than a second method (Method 2).
Each method was tested ten (10) times, with, yielding the following values:
Method
1
Mean (ppm)
6.7
Standard Deviation (ppm)
0.8
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Tutorial 4 Hypothesis Testing
2
8.2
1.2
At α = 0.05, can we support the researcher’s claim?
ANSWERS
1. H 0 :   RM 69.21
H1 :   RM 69.21 , Accept H o
2. H 0 :   240mg
H1 :   240mg , Reject H o
3. H 0 :   84 month
H1 :   84 month Accept H o
4. H 0 :   11.52 inches
5. H 0 :   RM 350
6. H 0 :   75
7. H 0 : p  0.23
H1 :   11.52 inches , Reject H o
H1 :   RM 350 , Accept H o
H1 :   75 , Accept H o
H1 : p  0.23 , Accept H o
8. H 0 : p  0.3
H1 : p  0.3 , Reject H o
9. H 0 : 1  2
H1 : 1  2 , Accept H o
10. H 0 : 1  2
H1 : 1  2 , Reject H o
11. H 0 :   2000 hours
12. H 0 : p1  p2
13. H 0 : p  0.80
14. H 0 : 1  2
15. H 0 :   22.2
H1 :   2000 hours , Accept H o
H1 : p1  p2 , Accept H o
H1 : p  0.80 , Accept H o
H1 : 1  2 , Accept H o
H1 :   22.2 , Accept H o
16. H 0 : 1  2
H1 : 1  2 , Reject H o
17. H 0 : p1  p2
H1 : p1  p2 , Reject H o
18. H 0 : p  0.95
19. H 0 : 1  2
20. H 0 : p  0.80
H1 : p  0.95 , Reject H o
H1 : 1  2 , Accept H o
H1 : p  0.80 , Accept H o
21. H 0 : 1  2
H1 : 1  2 , Accept H o
22. H 0 : p2  p1
H1 : p2  p1 , Reject H o
23. H 0 : 1  2
H1 : 1  2 , Reject H o
24. H 0 :  2  0.32 ounces
25. H 0 :  2  0.92 minutes
26. a. H 0 :  12   22
b. H 0 :  32   22
27. H 0 :  12   22
H1 :  2  0.32 ounces , Reject H o
H1 :  2  0.92 minutes , Accept Ho
H1 :  12   22 , Reject H o
H1 :  32   22 , Accept H o
H1 :  12   22 , Accept Ho
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