Statistics For Environmental Planning And Management Question Paper
Statistics For Environmental Planning And Management
Course:Bachelor Of Environmental Planning And Management
Institution: Kenyatta University question papers
Exam Year:2009
KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
ENVIRONMENTAL PLANNING AND MANAGEMENT
EPM 344: STATISTICS FOR ENVIRONMENTAL PLANNING AND
MANAGEMENT
DATE: Monday 21st December, 2009 TIME: 2.00 p.m. – 4.00 p.m.
INSTRUCTIONS
Answer question ONE and any other TWO. Maximum marks for each part of a
question are as indicated.
1.
a)
Define the following terms as used in statistics:
i)
Significance level of a test
ii)
Type
II
error
iii)
The
p-value
of
a
test
[5
marks]
b)
Using suitable examples, distinguish between ordinal and interval scales
of
measurement.
[10
marks]
c)
The following table shows the frequency distribution of masses of articles
packaged by a company:
Mass in grams 100 - 104 105 - 109 110 - 114 115-119
120-124
125-129
130-134
Frequency
12 18 24 32 19 11 7
i)
Calculate the mean mass of the articles and the standard deviation
ii)
Estimate the median value of the articles
iii)
Comment on your results
[15 marks]
2.
a)
A sample of size 40 yields the following sorted data. Note that the second
largest number is x-ed.
14.1 46.0 49.3 53.0 54.2 54.7 54.7 54.7 54.8 55.4 57.6 58.2 58.3 58.7 58.9 60.8 60.9 61.0 61.1 63.0
64.3 65.6 66.3 66.6 67.9 70.1 70.3 72.1 72.4 72.9 73.5 74.2 75.3 75.4 75.9 76.5 77.0 x
88.9
Page 1 of 4
i)
Calculate range, IQR, and median of these data.
ii)
Given that the mean of these data is 63.50 and the standard
deviation is 12.33, what proportion of the data lie within one
standard deviation of the mean?
iii)
How does your answer to (b) compare to the empirical rule
approximation? [10
marks]
b)
It is thought that the incidence of asthma in children is associated with the
volume of traffic in the area where they live. Two surveys of children
were conducted: one in an area where the volume of traffic was heavy and
the other in an area where the volume of traffic was light. The following
table shows the number of children in the survey who had asthma and
those who did not have asthma
Asthma
No
Asthma
Heavy traffic
52
58
Light traffic
28
62
Use a chi-square test at the 5% level of significance, to determine whether
the incidence of asthma in children is associated with the volume of traffic
in
the
area
where
they
live.
[10
marks]
3.
a)
The weight of fat in a digestive biscuit is known to be normally
distributed. A researcher conducted an experiment in which the weight of
fat, in grams, was measured in each of a random sample of 10 digestive
biscuits. The following results were obtained:
S x = 31.9
S(x – mean of x)2 = 1.849
i)
Construct a 99% confidence interval for the mean weight.
[5 marks]
ii)
Comment on a claim that the mean weight is 3.5 grams.
[2 marks]
Page 2 of 4
iii)
If 99% confidence intervals were constructed in a sample of 200,
how many would you expect not to contain the population mean?
[2 marks]
b)
Independent random samples were selected from two populations. Below
are summary statistics.
Pop.
Mean
Standard deviation
Sample size
1 62.00
10.00
17
2 54.00
6.00
10
i)
Construct the 95% confidence interval for µX – µY
ii)
Obtain the P-value for the alternative µX ? µY
[11 marks]
4.
The table shows the times taken, y minutes, for a wood glue to dry at different air
temperatures, xoC.
x 10 12 15 18 20 22 25 28 30
y
42.9 40.6 38.5 35.4 33.0 30.7 28.0 25.3 22.6
i)
Calculate the equation of the least squares regression line y on x.
[4 marks]
ii)
Estimate the time taken for the glue to dry when the air temperature is
21oC.
iii)
Calculate the value of the product moment correlation coefficient between
x and y and give a comment.
[20 marks]
5.
a)
Fifty students take mid semester and final examinations. On the mid
semester, the mean score is 45.0 and the standard deviation is 7.00. On
the final examination, the mean score is 85.0 with a standard deviation of
14.00. The correlation coefficient of the two scores is 0.64. Obtain the
least squares regression line for using the final exam score to predict the
mid semester exam score.
[5 marks]
Page 3 of 4
b)
Distances to waste disposal site is known to have a standard deviation of
2.5m. Due to population increase, it is believed that the mean distance is
not equal to the expected distance of 34.5m. In an experiment set up to
investigate this scenario, the distances to waste disposal sites of a random
sample of 50 households were measured. The mean distance of this
sample is 35.1m. Investigate the belief at the 5% level of significance.
[6 marks]
c)
The management of a gymnasium claims that the mean cholesterol level
of those members who have held membership for more than one year is
3.8. A researcher believes that the management’s claim is too low and
investigates by measuring the cholesterol levels of a random sample of 7
such members with the following results:
4.2 4.3 3.9 3.8 3.6 4.8 4.1
Is there evidence, at the 5% level of significance, to justify the
researcher’s belief that the mean cholesterol level is greater than the
management’s claim? State any assumption that you make.
[9 marks]
……………………………………
Page 4 of 4
More Question Papers
Exams With Marking Schemes
Popular Exams
Mid Term Exams
End Term 1 Exams
End Term 3 Exams
Opener Exams
Full Set Exams
Return to Question Papers