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AGS520S - AGRICULTURAL STATISTICS - 2ND OPP - JUNE 2024 |
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1.1 Page 1 |
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n Am I BI A u n IVER s ITY
OF SCIEn CE Ano TECHn OLOGY
FACULTYOF HEALTH,NATURAL RESOURCESAND APPLIEDSCIENCES
DEPARTMENT OF AGRICULTURALSCIENCESAND AGRIBUSINESS
QUALIFICATION: BACHELOR OF SCIENCE IN AGRICULTURE
QUALIFICATION CODE: 07BAGA
LEVEL: 7
COURSE CODE: AGS520S
COURSE NAME: AGRICULTURALSTATISTICS
SESSION: JULY2024
DURATION: 3 HOURS
PAPER: 2
MARKS: 100
SECOND OPPORTUNITY/SUPPLEMENTARY EXAMINATION QUESTION PAPER
EXAMINER(S) DR DAVID UCHEZUBA
MODERATOR: MR ANDREW ROUX
INSTRUCTIONS
1. This paper consists of two sections: Section A has 15 multiple-choice questions and 5 True
or False questions. Section Bis made up of four essay-type questions.
2. Answer ALL questions in blue or black ink.
3. Start each question on a new page in your answer booklet.
4. Questions relating to this paper may be raised in the initial 30 minutes after the start of the
examination. Thereafter, students must use their initiative to deal with any perceived error
or ambiguities & any assumption made should be clearly stated.
THIS MEMO CONSISTS OF 13 PAGES {Including this front page)
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SECTION A
QUESTION 1 {20 Marks)
Consider a random variable X with the following probability distribution.
I~-40
Use the table to answer questions 1.1 to 1.5.
I :.15
1.1.
Find P( X < 4)
A.
0.50
B
0.70
C
0.60
D
0.40
1.2
Find P( X 2 8 )
A.
0.25
B
0.40
C
0.30
D
0.10
1.3
X <5
A.
0.00
B
0.50
C
0.60
D
0.70
1.4
Assume the claim that the mean weight of airline passengers (including hand luggage) is greater
than 43 kg per person. Identify the null and alternative hypothesis used to verify this claim.
A.
Ha : µ 2 43 kg, Ha : µ > 43 kg
B
Ha:µ 2 43 kg, Ha:µ< 43 kg
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C
Ha:µ~ 43 kg, Ha : µ > 43 kg
D
Ha : µ 43 kg, Ha : µ '?.43 kg
1.5
How many per cent under the normal curve lies between µ ± 2a-
A.
95
B
68
C
90
D
97
1.6
We committed a type II error, which means we.
A.
Rejected a true null hypothesis
B.
fail to reject a false null hypothesis
C.
Rejected a false alternative hypothesis
D.
fail to reject a true null hypothesis
Consider a random variable X with the following probabilities. Use the table to answer questions 1.7
to 1.10.
1.7 Find the probability that represents (x)
A.
0.02
B.
0.04
C.
0.14
D.
0.03
Given a random variable X which is normally distributed with mean 15 and variance 100. Answer
questions 1.8 and 1.10. Find
1.8
P(X < 20)
A.
0.3125
B.
0.5140
C.
0.0235
D.
0.6915
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1.9
P(X > 20)
A.
0.3085
B.
0.4415
C.
0.1235
D.
0.9120
1.10 P(l2 < X < 20)
A.
0.1110
B.
0.1022
C.
0.3094
D.
0.2120
1.11 Which of the following measures of central tendency can be used when a dataset has an
outlier?
A.
Mean
B.
Median
C.
Mode
D.
Variance
1.12 The weight of an object is an example of
A.
A continuous random variable
B.
A discrete random variable
C.
Ordinal random variable
D.
Both discrete and continuous random variables.
1.13
When do we collect data from the entire population in statistical research? Which statement
is incorrect?
A.
When the population is small
B.
When the population is available
C.
When a fund is available
D.
We never use the entire population
1.14 The narrower the confidence interval.
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A.
The higher the probability of committing a type I or II error.
B.
The lesser the probability of committing a type I or II error.
C.
The larger the t-statistics
D.
The larger the critical value
1.15 The skewness and kurtosis of a normal probability distribution are.
A.
S =3; K = 0
B.
S = O;K =3
c.
S = O;K = 0
D.
S = I; K = 3
TRUEOR FALSEQUESTION
Indicate whether the following statements are true or false.
1.16.
1.17.
1.18.
1.19
1.20
The variable weight is an example of a continuous random variable. True or False
If A is an event that a seed sown will germinate and Bis an event that a seed sown
will not germinate, then events A and Bare mutually exclusive. True or False
The z-distribution table has both negative and positive values. True or False.
The mean is sensitive to extreme values (outliers). True or False.
If the null is rejected, the alternative is true. True or False
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SECTION B
QUESTION 2 {20 Marks)
2.1.
The term test scores of students enrolled in statistics classes were recorded as follows.
Calculate the following
2.1.1 Arithmetic mean
2.1.2. Mode
2.1.3. Variance
2.1.4. Standard deviation
2.1.5. Coefficient of variation
(2 Marks)
(2 Marks)
(2 Marks)
(2 Marks)
(2 Marks)
2.2.
2.3.
2.3.1.
2.3.2.
2.3.3.
2.3.4.
2.3.5.
How high should a doorway be if 95% of men will fit through it without bending or bumping
their heads? Find the 95th percentile of heights of men that passthrough the average doorway if
the heights of men are normally distributed with a mean of 69 inches and a standard deviation
of 2.8 inches.
(5 Marks)
Assume that the readings on the thermometers are normally distributed with a mean of 0°C-
and a standard deviation of 1°c. Find the indicated probabilities, where z is the reading in
degrees.
P(-1.96 < Z < 1.96)
(I Mark)
P(z < 1.645)
(I Mark)
P(z < -2.575 or z > 2.75)
(I Mark)
P(z <-1.96 or z > 1.96)
(I Mark)
P(z < -1.00 or z < -0.50)
(I Mark)
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QUESTION 3 {20 Marks)
3.1.
A manufacturing company estimates that its maximum daily demand for electricity during the
coming few weeks can be approximated by a normal distribution with mean 1000 kw and
standard deviation of 10 Kw
3.1.1.
Find the probability that the maximum demand for electricity will exceed 120 Kw on a given day.
(5 Marks)
3.1.2.
Find the probability that, on a given day, the maximum demand for electricity is lessthan 85 Kw.
(5 Marks)
3.2.
Find the probability that a given day's demand for electricity will exceed 95 Kw. (5 Marks)
3.3.
Find the probability that the maximum dailydemand for electricity will fall between 90 Kw
and 95 Kw
(5 Marks)
QUESTION 4 {20 Marks)
4.1. The frequency distribution table below gives the number of iPods sold by a shop on each of
30 days.
iPods sold
f
5-9
3
10-14
6
15 -19
8
20 -24
8
25 -29
5
30
Calculate the following.
4.1.1 The class mid-points.
4.1.2. The relative frequency.
4.1.3. The cumulative frequencies.
(2 Marks)
(2 Marks)
(2 Marks)
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4.1.4.
4.1.5.
The relative frequency percentages.
The cumulative frequency percentages.
(2 Marks)
(2 Marks)
4.2.
In a sample of 200 people, 84 had blood type 0, 88 had blood type A, 20 had blood type B,
and 8 had blood type AB. Set up a probability distribution table and answer the following.
4.2.1.
4.2.2.
4.2.3.
4.2.4.
4.2.5.
What is the probability that a person has blood type 07
(2 Marks)
What is the probability that a person has blood type A or blood type B?
(2 Marks)
What is the probability that a person has neither blood type A nor blood type 0? (2 Marks)
What is the probability that a person does not have blood type AB?
(2 Marks)
What is the probability that a person has a blood type A?
(2 Marks)
QUESTION 5 (20 Marks)
5.1.
An experiment to determine the level of potency of two pesticide labels was conducted. An
analysis of the variance table for the experiment is given below. Calculate the values of the
missing highlighted blocks.
Source of variation
Treatment
Error
Total
Sum of squares
60.40
437.60
A
Degrees of Freedom
2
4
B
Mean square
C
D
F-Test
E
(10 Marks)
5.2.
Company officials were concerned about the length oftime a particular drug product retained its potency.
A random sample of n 1 = 10 bottles of the product was drawn from the production line and analysed for potency.
= A second sample of n2 10 bottles was obtained and stored in a regulated environment for one year.
Readings obtained from each sample were recorded. Suppose we let µ1 denote the mean potency for all bottles that
might be sampled coming off the production line and µ2 denote the mean potency for all bottles that may be retained
for one year.
5.2.1
Estimate the differences in the mean µ1 - µ2 by using a 95 % confidence interval. Use the following
summary of the data>
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Summary
n
X
s
5.2.2. Interpret your result
Fresh
10
10.37
0.3234
STATISTICALFORMULA
Stored
IO
9.83
0.2406
(8 Marks)
(2 Marks)
0-2 = (x-x")2
N-I
u=
N-I '
z=-- x-µ
a
'
z--
x-µ-
a-X
X
_-
x-µ-
X
a
'
a (x-x) 2
=-'-----'-
N-I '
t = -'--(x_--'-µ-'--)
x-x
a=--,
n-I
N-I
t=----x'---µ
z=-- x-µ
a
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1.10 Page 10 |
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STATISTICALTABLES
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2 Pages 11-20 |
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2.1 Page 11 |
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Strindrd ~hrl',111CJ,IumulrttiveProl) bility Table
cur11·uJ1v&pr~I
torPQ'illTIV?E- ~I_98.w an~ll'l'llW '.(j Cft,{m·b$fe:
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The Chi-Square Distribution
__- ____,, .,;--"I
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,--
- -··1·}9-T-ll ,----
i. -41IJ !l
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