ST130: Basic Statistics
Faculty of Science, Technology & Environment
School of Computing, Information & Mathematical Sciences
Final Examination
Semester II, 2017
Mode: Face to Face/ Online
Duration of Exam: 3 hours + 10 minutes
Reading Time: 10 minutes
Writing Time: 3 hours
Total marks: 100
INSTRUCTIONS:
1. This exam has FIVE (5) questions of 20 marks each and all are compulsory.
2. Write your answers in the answer booklet provided.
3. Start each question on a new page.
4. Show all necessary working. Partial marks will be awarded for partially correct answers.
5. There are SIX (6) pages in this exam paper (including this cover page).
6. This exam is worth 50% of the overall mark. The minimum exam mark is 40/100.
7. You may use a NON PROGRAMABLE calculator.
8. Eton Statistical Table and Formula Sheet are provided.
ST130 FINAL EXAMINATION
Question 1
SEMESTER II, 2017
Start on a new page
[10 + 6 + 4 = 20 marks]
(A) A USP biologist conducted an experiment in which a sample of 30 beetles (of a particular species)
was weighed before and after exposure to an insect virus. The purpose of the experiment was to
establish whether the virus was effective for biological control of beetles. The following weight
(mg) was recorded before exposure to an insect virus.
380 381 384 399 400 402 402 405 410 415 416 418 418 419 423
425 425 425 429 433 437 438 438 441 442 447 448 449 449 450
(i)
Construct a grouped frequency distribution table with 5 classes using the lowest value in the
data set as the lower class limit of the first class. Also show in the table the class boundaries
of each class.
(ii)
Construct an ogive for the distribution.
(iii) Using the graph above to show how many beetles weigh less than 439 mg.
(4+4+2=10 marks)
(B) The scores in the first test of all 25 statistics students are presented below.
Score
Frequency
40.5-45.5
3
45.5-50.5
8
50.5-55.5
10
55.5-60.5
3
60.5-65.5
1
Calculate the following.
(i)
The approximate mean for the distribution.
(ii) The standard deviation.
(3+3=6 marks)
(C) The following data give the weights (in kg) gained by 14 members of a health fitness at the end of
two months after quitting the club.
1
3
2
2
10
4
1
5
Construct a box plot for the data.
Page 2 of 6
4
6
3
2
4
3
ST130 FINAL EXAMINATION
Question 2
SEMESTER II, 2017
Start on a new page
[2 + 3 + 4 + 6 + 5 = 20 marks]
(A) A card is picked from the pack of card, what is the probability that the card is red?
(B) Jerry is taking a statistics course ST130 and a marine course MS111. She estimates her probability
of passing ST130 at 0.4 and MS111 at 0.6 and she estimates her probability of passing both
courses at 0.8. What is her probability of passing ST130 or MS111?
(C) A box contains 12 light bulbs, of which 5 are defective. All bulbs look alike and have equal
probability of being chosen. Two lights are selected with replacement. What is the probability that
exactly 2 are defective?
(D) A survey on who smokes more, males or females was conducted using a sample of 360 USP
Laucala campus students. The two way table below shows the result.
Don’t smoke
Smoke
Total
(i)
Female
153
16
169
Male
164
27
193
Total
317
43
360
In a random selection of a student from the study population, what is the probability that the
student is a smoker given that the student is a female?
(ii) What is the proportion of smokers for the entire sample?
(3+3 =6 marks)
(E)
A USP taxi based driver estimates that his earnings are $240 on a fine day and $320 on a wet day.
What are his expected earnings on a day with probability of rain of 0.45?
Question 3
Start on a new page
(A) A soccer team has a probability of
[4+9+3+4= 20 marks]
3
of winning any game that it plays. In a season of 10 games,
5
what is the probability that the team wins exactly 6 games?
(B) A market gardener in Tonga sells cabbages to a supermarket. She claims that the weights of the
cabbages have a normal distribution with a mean weight of 1200 grams and a standard deviation of
50 grams.
Page 3 of 6
ST130 FINAL EXAMINATION
(i)
SEMESTER II, 2017
A cabbage is chosen at random, calculate the probability that its recorded weight is less than
1190 grams.
(ii)
A consumer officer for the supermarket checks the gardener’s claim by weighing 40 of the
cabbages. If the market gardener’s claim is true, calculate the probability that the 40
cabbages have a mean weight of less than 1190 grams.
(4+5=9 marks)
(C) A health care professional wishes to estimate the birth weights of infants. How large a sample must
be obtained if she desires to be 90% confident that the true mean is within 2 ounces of the sample
mean? Assume   8 ounces.
(D) A sociologist found that in a sample of 50 retired men, the average number of jobs they had during
their lifetimes was 7.2. The population standard deviation is 2.1. Find the 99% confidence interval
of the mean number of jobs.
Question 4
Start on a new page
[6+6+8=20 marks]
(A) The average local cell phone call length was reported to be 2.27 minutes. A random sample of 20
phone calls showed an average of 2.98 minutes in length with a standard deviation of 0.98 minute.
At   0.05 can it be concluded the average differs from the population average?
(B) A recent survey found that 68.6% of the population owns their homes. In a random sample of 150
heads of households, 92 responded that they owned their homes. At the   0.01 level of
significance, does that suggest a difference from the national proportion?
(C) In a study of women science majors, the following data were obtained on two groups, those who
left their profession within a few months after graduation (leavers) and those who remained in
their profession after they graduated (stayers). At   0.05, test the claim that those who stayed
had a higher science grade point average than those who left.
Leavers
X 1  3.16
Stayers
X 2  3.28
1  0.52
 2  0.46
n1  103
n2  225
Page 4 of 6
ST130 FINAL EXAMINATION
Question 5
SEMESTER II, 2017
Start on a new page
[5+5+10=20 marks]
(A) The data below indicate the state gas tax in cents per gallon and the fuel use per registered
vehicle (in gallons). Is there a significant relationship between these two variables? Use the
sample correlation coefficient to be r  0.367.
Tax
21.5
23
Usage
1062 631
18
24.5
26.4
19
920
686
736
684
(B) The 2010 winter Olympics final medal counts for the top four nations are shown below. At the
  0.1 level of significance can it be concluded that the type of medal won was dependent upon
2
the competing country? Use the test value to be   6.657.
Gold
Silver
Bronze
9
10
14
9
15
13
7
8
13
7
5
6
United States
Germany
Canada
Norway
(C) The amount of sodium (in milligrams) in one serving for a random sample of three different kinds
of food is listed below.
Condiments Cereals Desserts
270
130
230
180
80
70
200
260
220
290
290
200
320
140
100
180
250
250
300
360
300
160
Complete the ANOVA table given below in the answer booklet.
Source
Between
Error
Total
Sum of squares
d.f.
   END OF EXAM   
Page 5 of 6
Mean square
F
ST130 FINAL EXAMINATION
SEMESTER II, 2017
FORMULAE
1.  
 fX
m
and
2 
 fX
2
m
  fX 

2
m
N
.
N
N
2. P ( A  B )  P ( A)  P ( B ). If A and B are independent.
3. P( A  B )  P ( A)  P ( B A). If A and B are dependent.
4. P  A  B   P ( A)  P ( B )  P ( A  B ).
5. P( B A) 
P( A  B)
.
P( A)
6.   E ( X )   X P ( X ) and  2   X 2 P ( X )   2 .
7. P( X )  nC X p X q n  X .

8. X  z 2
n

   X  z 2
n
.
z 
9. n     2  .
 E 
X 
10. t 
, d . f  n  1.
s/ n
pˆ  p
11. z 
.
pq / n
2
12. z 
X
1
 X 2    1  2 
 12
n1
13. t  r
14. S
2
B

 22
.
n2
n2
, d . f  n  2.
1 r2
n X

i
i
 X GM 
k 1
2
2
W
, S
  n  1 S

  n  1
i
2
i
and F 
i
Page 6 of 6
S B2
SW2