Get premium membership and access revision papers, questions with answers as well as video lessons.
Acs 206: Statistics 1 Question Paper
Acs 206: Statistics 1
Course:Bachelor Of Science In Agriculture
Institution: South Eastern Kenya University question papers
Exam Year:2012
SOUTH EASTERN KENYA UNIVERSITY
UNIVERSITY EXAMINATIONS 2012/2013
SECOND YEAR FIRST SEMESTER EXAMINATION FOR THE
DEGREE OF BACHELOR OF SCIENCE IN AGRICULTURE,
BACHELOR OF SCIENCE IN RANGE MANAGEMENT AND
BACHELOR OF SCIENCE IN HORTICULTURE
ACS 206: STATISTICS 1
Date: 15th August 2012 Duration: 2 hours
Instructions:
Answer questions 1 and any other 3 questions.
Question one
a) Define the following terms.
i. Descriptive statistics.
ii. ii) Inferential statistics. (2marks)
b)
i. Outline four causes of sampling errors. (4marks)
ii. Highlight three benefits of stratified random sampling. (3marks)
c) Given the set of numbers, 12, 6, 7, 9, 15, 13, 11 and 18. Find the variance (6marks)
d) The yields obtained by farmers in certain season were as follows.
Yields (Bags of maize) 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79
Number of farmers 4 10 16 19 8 3
Plot a histogram and a frequency polygon to depict that data. (5marks)
e) In a certain university college, the students are classified according to their faculty.
The students composition is in the following order.
Faculty No Of students
Arts 3,200
Science 1,800
Commerce 900
If one uses proportional allocation to select a stratified random of 200 students, how large a
sample must be taken from each stratum. (4marks)
f) The number of parts for a particular spare parts in a factory was found to vary from day to
day. In a sample study the following information was obtained.
Day Mon Tue Wed Thur Fri Sat
No. of parts demanded 1124 1125 1110 1120 1126 1115
Test the hypothesis that the number of parts demanded does not depend on the day of the
week at 5% level of significance. (7 marks)
g) On average a posho mill breaks down eight times during a week (Monday to Friday ).
Assuming that the number of breakdowns can be modeled by a poison distribution, find
the probability that it breaks down.
i) Five times in a given week. (3marks)
ii) Once on Monday. (3marks)
iii) Eight times in a fortnight. (3marks)
Question two
a) State and explain five importance of statistics to a firm manager. (10marks)
b) For a group of 200 farmers the mean yield and standard deviation were found to be 40
and 15 respectively. Later it was discovered that the yields 43kg and 35kg were misread
as 34kg and 53kg respectively. Find the correct mean and correct standard deviation
corresponding to correct figures. (7marks)
c) An analysis of salaries paid to workers of 2 firms A and B belonging to the same industry
gives the following.
Firm A Firm B
No. of workers 400 500
Average monthly salaryl ( £) 196 185
Variance of distribution. 81 100
By calculating the co-efficient of variation, determine which firm is more consistent in
salaries. (3marks)
Question Three.
The following is the record of ages of VCT attendance in one of the centers.
15 25 35 25 28 11 55 19 19 27 22 20
61 48 42 22 38 34 40 38 22 35 60 24
24 19 22 25 58 30 39 25 40 41 46 21
43 38 34 47 23 28 21 23 30 17 20 31
40 19 20 21 29 26 25 27 35 41 30 13
a) Classify the data above by constructing a frequency distribution, taking 10 – 14 as the first class. (4marks)
b) Calculate.
i) Arithmetic mean. (3marks)
ii) Median. (4marks)
iii) Mode. (4marks)
iv) Standard deviation of the distribution. (5marks)
Question four.
a) Define the following terms.
i) Stochastically independent events. (2marks)
ii) Mutually exclusive events. (2marks)
b) A university student studying the employment situation in a certain town found out that
the probabilities of males and females who are employed is as shown in the table below.
Employment Un employment
Males 0.40 0.10
Females 0.425 0.025
Suppose an employed person is chosen at random, find the probability that the person
selected is.
i) Male. (3marks)
ii) Female. (3marks)
c) Eggs are packed in a box of 500. On average 0.7% of the eggs are found broken when
unpacking, using poison approximation to binomial distribution, find the probability that
in a box of 500 eggs;
i) Exactly 3 are broken. (7marks)
ii) Atleast 2 are broken.
d) The probability that somebody supports the new constitution is 0.6. Find the probability
that in a randomly selected sample of 8 people, more than 5 will vote ‘yes’. (3marks)
Question five
a) 80% of a population is known to have a particular eye disorder. If 12 people are waiting
to see the nurse, what is the most likely number to have the eye disorder. (6marks)
b) The time taken by the salesman to deliver milk to the market is normally distributed with
mean 12 minutes and a standard deviation of 2 minutes. He delivers milk every day.
Estimate the number of days during the year when he takes .
i) Longer than 15 minutes. (4marks)
ii) Less than ten minutes. (4marks)
iii) Between nine and 13 minutes. (4marks)
c) The heights of men in a certain club at a particular age follows a normal distribution with
mean 150.3cm and standard deviation 5. Find the probability that a somebody picked at
random has height less than 153cm. (2marks)
Question six
a) Define the following terms as used in sampling theory.
i) Sample.
ii) Attribute.
iii) iii) Target population. (3marks)
b) Differentiate between.
i) Sampling frame and sampling design.
ii) ii) Under-coverage and over-coverage. (4marks)
c) State and briefly explain the three types of sampling methods. (6marks)
d) The height of a new variety of sunflower can be modeled by a normal distribution with
mean 2m and standard deviation of 40cm. A random sample containing 50 sunflowers is
taken and the mean height calculated.
i) What is the probability that the sample mean lies between 195cm and 205cm.
(3marks)
ii) A hundred such samples each with 50 observations are taken. In how many of these
would you expect the sample mean to be greater than 210. (4marks)
More Question Papers
Popular Exams
Return to Question Papers