Supp Revision
Q1
You are approached by a person in the street who asks you to participate in a study
on life insurance by answering a number of questions. The method of sampling
which has been used to select you is
a) Convenience sampling
b) Probability sampling
c) Simple random sampling
d) Systematic sampling
e) None of the above
Q2
It is known that 13% of the South African population suffers from dry eyes.
A random sample of 1200 high school students was selected from the
Durban area. It was found that 6% of these students suffer from dry eyes.
Which of the following statements is true?
a)The value “6%” referred to is a parameter.
b)The value “6%” a statistic
c) The sample frame and the population of interest are the same.
d)The sample indicates that 6% of all high school students suffer from dry
eyes.
e)All the statements above are false.
Q3
The levels of measurement for the variables.
i. The level of study of university students (1st year, 2nd year etc) that drink coffee
daily.
ii. The number of years spent studying at university.
iii. The age of a student
a) i) ratio
ii) nominal
iii) ratio
b) i) ordinal
ii) ordinal
iii) ratio
c) i) ordinal
ii) ratio
iii) ratio
d) i) ratio
ii) ordinal
iii) interval
e) i) nominal
ii) interval
iii) ratio
Q4
If we have a histogram graph that shows the age of students registered for STAT130
and it is positively skewed (Right-skewed distribution) with a median of 22. What
can be said about the possible value of the mean?
a) It can be exactly the same as the median
b) It will be less than 22
c) It will be more than 22
d) Without the actual data values nothing can be said about the value of the
sample mean.
e) None of the above
Q5
The following data represents the number of hours students spent studying for a
final exam: 21 26 13 31 26 13 27 46 33 47 32 35 71 52 22
Create a stem-and-leaf plot for this data. Then, describe the shape of the
distribution of study hours based on your stem-and-leaf plot.
a) Positively skewed
b) Symmetrical
c) Negatively skewed
d) Uniform
e) None of the above
Q6
The number of teachers strikes in the last 14 years are shown in the table below.
Which of the following Microsoft excel command I can use to calculate the
variance of the number of strikes is?
a) = VA.S (A1:G2)
b) =VAR.P(A1:G2)
c) =VARIANCE (A1:G2)
d) =VAR.S(A1:G2)
e) =VAR.S(A1:G1;A2:G2)
Q7
The number of teachers strikes in the last 14 years are shown in the table below.
What is the median number of teachers strikes in the last 14 years?
a) 7.5
b) 14
c) 10.14
d) 10.5
e) 9.0
Q8
The number of teachers strikes in the last 14 years are shown in the table below.
Which of the following Microsoft excel command I can use to calculate the median
of the number of strikes is?
a) = QUARTILE.EXC(A1:G2; 2)
b) = QUARTILE(A1:G2; 50)
c) = QUARTILE.INC(A1:G2; 25)
d) = QUART.EXC(A1:G2; 0,2)
e) = QUARTILE(A1:G2; 0,5)
Q9
The frequency distribution below gives the scores of students in STAT130
exam last year.
What shape does the data appear to have?
a)negatively skew
b)bimodal
c) bell-shaped
d)uniform
e)positively skew
Q10
The frequency distribution below gives the scores of students in STAT130
exam last year.
What is the approximate average test score?
a)30.13
b)50.13
c) 35.13
d)40.31
e)296
Q11
The frequency distribution below gives the scores of students in STAT130 exam last
year.
What is the value for 𝑷𝟔𝟎 ?
a)38.95
b)55.55
c) 48.95
d)80.95
Q12
The frequency distribution below gives the scores of students in STAT130 exam last
year.
If a student is chosen at random, what is the probability that their exam test score was at least 50
marks?
a) 0.3721
b) 0.1130
c) 0.6279
d) 0.1213
Q13
The heights of Team A and Team B players were measured in centimetres:
Average
Variance
Team A
206
2
Team B
210.5
1.1
Which of the following statements is true?
a) Team A is more consistent in height measurements as it has a lower relative variability
compared to Team B.
b) Team A is more consistent in height measurements as it has a higher relative variability
compared to Team B.
c) The variability of the two teams cannot be compared because the sample sizes are the same.
d) Team B has a lower coefficient of variation than Team A, indicating that Team B's height
measurements are more consistent.
e) None of the above.
Q14
A sample of 1000 couples were interviewed and asked how much they spent on
groceries each week. The average amount was found to be R500 with a standard
deviation of R75. It was also found that the data was bell shaped. Approximately
how much money could you expect to spend between R425 and R575 on groceries
each week?
a)R950
b)R500
c) R970
d)R680
e)R160
Q15
A survey was conducted to assess students' sleep patterns and duration. Participants were asked
about their usual bedtime and wake-up time. The box plots below display the findings.
Q15
Which of the following statements is false?
a) People seem to sleep longer on Friday and Saturday nights
b) Less than half of the participants slept before 6 on Tuesday.
c) It can be deduced that the participants average length of sleep on Tuesday and
Wednesday are the same.
d) 25% of the participants only slept for 2 hours on Monday.
e) Somebody didn’t go to bed on Friday night.
Q16
Suppose you have the following sample space:
𝑆 = 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 ,60
Define the following 3 events on this sample space:
𝐴: The number is divisible by 10.
𝐵: The number is greater than 30.
𝐶: The number is not divisible by 5.
Find 𝑃 𝐴 ∩ 𝐶 ∩ 𝐵 ∪ 𝐴 .
a) 9 11
b) 0
c) 1
d)6 11
e) None of the above
Q17
Consider the Venn diagram below.
Which of the following represent the shaded area?
a)A ∪ B
b)A ∩ B
c) A ∪ B
d)A ∩ B
e)B ∩ A
Q18
At the Avonlea Country Club, swimming and playing bridge are two of the most
common activities. Eighty-two percent (82%) of the members play bridge, 75%
swim and 71% do both activities.
What is the probability of a member doing at least one of the activities?
a) 0.29
b) 0.86
c) 0.71
d) 0.14
e) 0.75
Q19
At the Avonlea Country Club, swimming and playing bridge are two of the most
common activities. Eighty-two percent (82%) of the members play bridge, 75%
swim and 71% do both activities.
If a swimming member is randomly selected, what is the probability that they also
play bridge?
a) 0.9467
b) 0.7111
c) 0.8659
d) 0.1400
e) 0.7501
Q20
An e-commerce platform records the following data for customers who purchase
gadgets:
Did not purchased
Purchased Electronics
Electronics
Regular Customers
147
281
First-Time Customers
194
178
What is the probability of electronic devises being purchased by customers?
a) 0.4650
b) 0.4263
c) 0.1838
d) 0.5350
e) 0.2425
Q21
An e-commerce platform records the following data for customers who purchase
Purchased
Did not purchase
gadgets:
Electronics
Regular
Customers
First-Time
Customers
Electronics
147
281
194
178
If electronic devices were not purchased by customers, what are the odds in favour of a
customer being a regular customer?
a) 1.15 : 1
b) 1 : 1.93
c) 1 : 2.63
d) 1.35 : 1
e) 1 : 0.63
Q22
Sleep apnoea is a disorder that interrupts breathing and can awaken sufferers as
often as five times an hour. Sleep apnoea is not easily diagnosed because it usually
causes loud snoring. It is known that 15% of adults have sleep apnoea. 84% of
adults that suffer from sleep apnoea snore loudly, whereas, only 40% of adults
without sleep apnoea snore loudly.
What is the probability that an adult has sleep apnoea and snores loudly?
a) 0.107
b) 0.126
c) 0.214
d) 0.400
e) 0.786
Q23
Sleep apnoea is a disorder that interrupts breathing and can awaken sufferers as
often as five times an hour. Sleep apnoea is not easily diagnosed because it usually
causes loud snoring. It is known that 15% of adults have sleep apnoea. 84% of
adults that suffer from sleep apnoea snore loudly, whereas, only 40% of adults
without sleep apnoea snore loudly.
What is the probability that an adult snores loudly?
a) 0.448
b) 0.466
c) 0.475
d) 0.080
e) 0.214
Q24
Sleep apnoea is a disorder that interrupts breathing and can awaken sufferers as
often as five times an hour. Sleep apnoea is not easily diagnosed because it usually
causes loud snoring. It is known that 15% of adults have sleep apnoea. 84% of
adults that suffer from sleep apnoea snore loudly, whereas, only 40% of adults
without sleep apnoea snore loudly.
If an adult complains to his/her doctor that his/her loud snoring is waking him/her up often,
what is the probability that he/she has sleep apnoea?
a) 0.233
b) 0.466
c) 0.212
d) 0.032
e) 0.270
Q25
Inside a box are a R10 note, a R20 note, a R50 note and a R100 note. Consider the
experiment in which two notes are drawn from the box without replacement. Let 𝑋 be the
random variable that gives the total amount of money drawn. The probability
distribution/mass function for 𝑋 is
a) .
b) .
c) .
d) .
e) None of the above
Q26
Consider the Cumulative distribution function below where 𝑐 and 𝑘 are constants.
What are the possible values for 𝑐 and 𝑘 are
a) 𝑐 = 0.12 and 𝑘 = 0.9
b) 𝑐 = 0.31 and 𝑘 = 0.85
c) 𝑐 = 0.28 and 𝑘 = 0.7
d) 𝑐 = 0.15 and 𝑘 = 0.3
e) 𝑐 = 0.09 and 𝑘 = 0.52
Q27
A research journal reports that 40% of ducks in a particular region have bird flu.
You assume this is true and randomly select 15 ducks from this region.
What is the probability that 5 to 8 of the ducks have bird flu?
a) 0.5018
b) 0.9050
c) 0.4032
d) 0.6877
e) 0.2173
Q28
A research journal reports that 40% of ducks in a particular region have bird flu.
You assume this is true and randomly select 15 ducks from this region.
What is the probability that at least 80% of the ducks have bird flu?
a) 0.0019
b) 0.0003
c) 0.3980
d) 0.6482
e) 0.3518
Q29
A research journal reports that 40% of ducks in a particular region have bird flu.
You assume this is true and randomly select 15 ducks from this region.
Which one of the following commands can you use in Microsoft Excel to calculate
the probability that at least 12 of the ducks have no bird flue?
a) = 1 − 𝐵𝐼𝑁𝑂𝑀. 𝐷𝐼𝑆𝑇 11 ; 15 ; 0,40 ; 𝐹𝐴𝐿𝑆𝐸
b) = 𝐵𝐼𝑁𝑂𝑀. 𝐷𝐼𝑆𝑇 12; 15 ; 0,60 ; 𝑇𝑅𝑈𝐸
c) = 1 − 𝐵𝐼𝑁𝑂𝑀. 𝐷𝐼𝑆𝑇 11 ; 15 ; 0,60 ; 𝑇𝑅𝑈𝐸
d) = 𝐵𝐼𝑁𝑂𝑀. 𝐷𝐼𝑆𝑇 11 ; 15 ; 0,40 ; 𝑇𝑅𝑈𝐸
e) = 𝐵𝐼𝑁𝑂𝑀. 𝐷𝐼𝑆𝑇 12; 15 ; 0,400 ; 𝐹𝐴𝐿𝑆𝐸
Q30
On average, 5 customers arrive at McDonald’s to buy takeaway every hour. The
arrivals are random and independent.
The Excel function to find the probability that 2 to 5 customers arrive in an
hour:
a) = 𝑃𝑂𝐼𝑆𝑆𝑂𝑁. 𝐷𝐼𝑆𝑇 5; 2,5; 𝑇𝑅𝑈𝐸 − 𝑃𝑂𝐼𝑆𝑆𝑂𝑁. 𝐷𝐼𝑆𝑇(2; 2,5; 𝑇𝑅𝑈𝐸)
b) = 𝑃𝑂𝐼𝑆𝑆𝑂𝑁. 𝐷𝑆𝑇 5; 5; 𝑇𝑅𝑈𝐸 − 𝑃𝑂𝐼𝑆𝑆𝑂𝑁. 𝐷𝐼𝑆𝑇(2; 5; 𝑇𝑅𝑈𝐸)
c) = 𝑃𝑂𝐼𝑆𝑆𝑂𝑁. 𝐷𝐼𝑆𝑇 5; 5; 𝑇𝑅𝑈𝐸 − 𝑃𝑂𝐼𝑆𝑆𝑂𝑁. 𝐷𝐼𝑆𝑇(1; 5; 𝑇𝑅𝑈𝐸)
d) = 𝑃𝑂𝐼𝑆𝑆𝑂𝑁 5; 5; 𝐹𝐴𝐿𝑆𝐸 − 𝑃𝑂𝐼𝑆𝑆𝑂𝑁. 𝐷𝐼𝑆𝑇(5; 5; 𝑇𝑅𝑈𝐸)
e) = 𝑃𝑂𝐼𝑆𝑆𝑂𝑁. 𝐷𝐼𝑆𝑇 5; 5; 𝐹𝐴𝐿𝑆𝐸 − 𝑃𝑂𝐼𝑆𝑆𝑂𝑁. 𝐷𝐼𝑆𝑇(2; 5; 𝐹𝐴𝐿𝑆𝐸)
Q31
On average, 5 customers arrive at McDonald’s to buy takeaway every hour. The
arrivals are random and independent.
If the server at the counter typically spends 3 minutes taking each customer’s
order, how long would you expect the server to spend taking orders from
customers in 4 hours?
a) 60 minutes
b) 45 minutes
c) 30 minutes
d) 120 minutes
e) 80 minutes
Q32
Find the value 𝑐, 𝑐 < 0 , such that the area under the standard normal
curve between 𝑐 and 0 is 0.2673. Find the corresponding value of Z?
a) -1.2600
b) -0.7300
c) 0.8962
d) 0.7300
e) 1.2600
Q33
The diagram below shows the probability distribution curves of three normal random variables:
𝑋1 , 𝑋2 and 𝑋3 .
Which one of the following statements is true?
a) The mean of 𝑋3 is smaller than the means of 𝑋1 and 𝑋2 .
b) 𝑋2 has the largest variance.
c) The median of 𝑋1 is the same as that of 𝑋2 .
d) All three random variables are only defined for values from –2.5 to 4.
e) The variances of 𝑋1 and 𝑋2 both equal 1.
Q34
The length of human pregnancies from conception to birth is normally distributed
with a mean of 266 days and a standard deviation of 16 days.
What is the probability that a pregnancy will last more than 220 days?
a)0.899
b)0.950
c) 0.885
d)0.998
e)None of the above
Q35
The length of human pregnancies from conception to birth is normally distributed
with a mean of 266 days and a standard deviation of 16 days.
It is recommended that if a pregnancy is less than 250 days the mother needs
go for checking. If a sample of 50 mothers is randomly chosen, approximately
how many would you expect to need to go for checking?
a) 7
b) 8
c) 9
d) 50
e) 12
Q36
The length of human pregnancies from conception to birth is normally distributed
with a mean of 266 days and a standard deviation of 16 days.
Only 30% of all pregnancies are longer than.
a)285.36 days
b)266 days
c) 178.98 days
d)274.32 days
e)200 days
Q37
The length of human pregnancies from conception to birth is normally distributed
with a mean of 266 days and a standard deviation of 16 days.
Suppose a random sample of sixty (60) mothers is taken. What is the probability
that their pregnancy days are between 260 and 270?
a)0.9732
b)0.0018
c) 0.9720
d)0.8534
e)0.9500
Q38
Ninety-two (92) percent of all UKZN students have siblings. If a random sample of
250 UKZN students is selected, what is the standard error of the sampling
distribution associated with the sample proportion, 𝑃 ?
a)
b)
c)
d)
0.92 0.08
250
0.92
0.08
250
0.92 0.08
250
0.92
250
e)None of the above
Q39
Over the last several years it has been found that 67% of customers at a particular
large grocery store request plastic packets to carry their groceries. A random
sample of 50 customers is taken.
What is the probability that the proportion of them that request plastic packets is
less than 0.6?
a) 0.1469
b) 0.8531
c) 0.8438
d) 0.0455
e) 0.7190
Q40
Over the last several years it has been found that 67% of customers at a particular
large grocery store request plastic packets to carry their groceries. A random
sample of 50 customers is taken.
What is the probability that the difference between sample proportion of
customers and the true proportion of customers who request plastic packets to
carry their groceries is no more than 0.05?
a) 0.4469
b) 0.1323
c) 0.5343
d) 0.5468
e) None of the above
Q41
A supermarket receives complaints that the mean content of “1 kilogram” sugar
bags that are sold by them is more than 1 kilogram. A random sample of 40 sugar
bags is selected from the shelves and the mean found to be 1.013 kilograms. From
past experience the standard deviation contents of these bags is known to be
0.025 kilograms. Test, at the 5% level of significance, whether this complaint is
justified.
𝐻0 will be rejected if the 𝑍0 test statistic is
a) greater than 3.289
b) less than –1.645 or greater than 1.645
c) less than –1.645
d) greater than 1.645
e) greater than 1.767.
Q42
A supermarket receives complaints that the mean content of “1 kilogram” sugar
bags that are sold by them is more than 1 kilogram. A random sample of 40 sugar
bags is selected from the shelves and the mean found to be 1.013 kilograms. From
past experience the standard deviation contents of these bags is known to be
0.025 kilograms.
Construct a 95% confidence interval for the mean content of the sugar bags.
a) ( 1.7842 ; 1.8063 )
b) ( 4.3729 ; 4.6057 )
c) ( 1.0052; 1.0208 )
d) ( 1.1036 ; 1.2339 )
e) None of the above.
Q43
Consider the example on the mean content of 500 ml cool drink bottles. The
standard deviation of the amount of cool drink in the bottles is 5 ml. Suppose it is
desired to estimate the mean content of the bottles with 95% confidence and an
error that is not greater than 0.8. What sample size is needed to achieve this
accuracy?
a) 500
b) 151
c) 205
d) 400
e) 180
Q44
An insurance company states that 90% of its claims are settled within 30 days. A
consumer group selects a random sample of 75 of the company’s claims to
perform a hypothesis test to see if the percentage could be smaller. The consumer
group finds that 62 of these insurance claims were settled within 30 days. A 5%
level of significance is used for the hypothesis test.
Which of the following pairs of hypotheses do you use for your test?
a) 𝐻0 : 𝑝 = 0.83 𝑣𝑠 𝐻1 : 𝑝 > 0.83
b) 𝐻0 : 𝑝 = 0.9 𝑣𝑠 𝐻1 : 𝑝 < 0.9
c) 𝐻0 : 𝑝 = 0.9 𝑣𝑠 𝐻1 : 𝑝 ≠ 0.9
d) 𝐻0 : 𝑝 = 0.9 𝑣𝑠 𝐻1 : 𝑝 > 0.9
e) 𝐻0 : 𝑝 = 0.83 𝑣𝑠 𝐻1 : 𝑝 = 0.83
Q45
An insurance company states that 90% of its claims are settled within 30 days. A consumer group
selects a random sample of 75 of the company’s claims to perform a hypothesis test to see if the
percentage could be smaller. The consumer group finds that 62 of these insurance claims were
settled within 30 days. A 5% level of significance is used for the hypothesis test.
The critical value used for the test is –1.645. What is the value of the test statistic and what
decision will be made?
a) The test statistic is 1.678 so reject 𝐻0 .
b) The test statistic is 2.117 so do not reject 𝐻0 .
c) The test statistic is –1.528 so do not reject 𝐻0 .
d) The test statistic is –1.678 so reject 𝐻0 .
e) The test statistic is –2.117 so reject 𝐻0 .
Q46
An insurance company states that 90% of its claims are settled within 30 days. A consumer group
selects a random sample of 75 of the company’s claims to perform a hypothesis test to see if the
percentage could be smaller. The consumer group finds that 62 of these insurance claims were
settled within 30 days. A 5% level of significance is used for the hypothesis test.
The consumer company constructs a 99% confidence interval for the true proportion of
insurance claims that are settled within 30 days. The confidence interval constructed is
a) ( 0.725 ; 0.928 )
b) ( 0.737 ; 0.916 )
c) ( 0.714 ; 0.939 )
d) ( 0.746 ; 0.907 )
e) none of the above.
Q47
A Type II error is made when
a) the alternative hypothesis is accepted when it is true.
b) the null hypothesis is rejected when it is false.
c) the alternative hypothesis is rejected when it is false.
d) the null hypothesis is rejected when it is true.
e) the null hypothesis is not rejected when it is false.
Q48
The lecturer for a Statistics module wants to find out if a student’s examination mark (Y) can be
predicted by their assignment mark (X). A random sample of 14 students was selected and their
marks were evaluated. The data is given below:
X
69
42
43
40
100 80
100 90
77
47
68
50
45
41
Y
77
66
65
65
80
78
70
60
67
61
59
58
71
Write down the line of best fit:
a) 𝑦 = 49.654 + 0.288𝑥
b) 𝑦 = 56.232 + 0.300𝑥
c) 𝑦 = 4.725 + 0.145𝑥
d) 𝑦 = 0.288𝑥 − 49.654
e) None of the above.
75
Q49
The lecturer for a Statistics module wants to find out if a student’s examination mark (Y) can be predicted
by their assignment mark (X). A random sample of 14 students was selected and their marks were
evaluated. The data is given below:
X
69
42
43
40
100 80
100 90
77
47
68
50
45
41
Y
77
66
65
65
80
78
70
60
67
61
59
58
71
75
Calculate and interpret the coefficient of determination for the marks data.
a) 𝑟 2 = 0.28, This means that there is a weak linear relationship between the examination mark and
assignment mark.
b) 𝑟 2 = 0.88, This means that 88% of the variability of the assignment mark can be explained by its
linear relationship with the examination mark.
c) 𝑟 2 = 0.88, This means that the assignment mark will be 0.88 marks more than the examination
mark.
d) 𝑟 2 = 0.08, This means that there is no relationship between the examination mark and assignment
mark.
e) 𝑟 2 = 0.08, This means that 8% of the variability of the assignment mark can be explained by its linear
relationship with the examination mark.
Q50
You want to buy a new car but know that cars lose their value as soon as they are driven off the
dealer’s lot/showroom. You used linear regression to get a better sense of how this decline
works. Using a random sample of cars, you found the following regression line
𝑦 = 410.45 − 45.6 𝑥
where 𝑥 is the age of the car (in years) and 𝑦 is the value of the car (in thousands of Rands).
Using this information, how much would you expect a 4 year old car to cost?
a) R 228050
b) R 592850
c) R 228050
d) R 399050
e) None of the above
Best of Luck