ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
(Department of Agricultural Sciences)
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Course: Statistics(794) Half CreditSemester: Spring, 2018
Level: M.Sc Hon,sLivestock ManagementTotal Marks: 100
Pass Marks: 40
ASSIGNMENT No. 1
Q.1.a)Describe the procedure for interval estimation about a population
proportion.(10)
b)In a random sample of 1215 animals, 62 exhibited a certain genetic
defect. Determine 95%confidence interval for the proportion of the
population displaying this defect and interpret the interval.(10)
Q.2.The following data give wing lengths of thirteen sparrows of various ages.(20)
Age (Days) / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15Wing Length(cm) / 1.4 / 1.5 / 2.2 / 12.4 / 3.1 / 3.2 / 3.2 / 3.9 / 4.1 / 4.7 / 4.5 / 5.2 / 5.0
i)Draw a scatter plot taking age on x-axix and wing length on y-axis. Does the relationship seem to be linear?
ii)Compute Coefficient of correlation (r) and interpret it.
iii)Fit a simple linear regression model on the given data and report the fitted equation.
iv)Test the slope of the equation = 0
v)Compute the value of coefficient of determination for the fitted model.
Q.3.a)In the field of livestock which areas is focus of research for the
improvement of livestock production?(10)
b)What is a design of experiment? Write down the three basic principles
of experimental design elaborating each with examples.(10)
Q.4.Four tropical feedstuffs were fed to a different lot of five baby chicks. The gains in weights were noted and are given below: (20)
Lot / 55 / 49 / 42 / 21 / 52Lot / 61 / 112 / 30 / 89 / 63
Lot / 42 / 97 / 81 / 95 / 92
Lot / 169 / 137 / 169 / 85 / 154
i)Prepare an analysis of variance table and test the hypothesis that means of all the lots are same. Use 1% level of significance.
ii)Which experimental design has been used in this experiment?
iii)Compare the average weight gain of lot four with average weight gain of other three lots.
iv)Give advantages and disadvantages of the design used.
Q.5.A study is made of amino acids in the hemolymph of millipedes. For a sample of four males and four females of each of three species, the following concentrations of the amino acid, alanine (in mg/100 ml), are determined: (20)
Category / Species-i / Species-2 / Species-3Male / 21.5 / 14.5 / 16.0
19.6 / 17.4 / 20.3
20.9 / 15.0 / 18.5
22.8 / 17.8 / 19.3
Female / 14.8 / 12.1 / 14.4
15.6 / 11.4 / 14.7
13.5 / 12.7 / 13.8
16.4 / 14.5 / 12.0
i)Which experimental design was used in this experiment?
ii)Test the hypothesis that there is no difference in the mean hemolymph alanine concentration among three species.
iii)Test the hypothesis that there is no difference between males and females in the mean hemolymph alanine concentration.
iv)Test the hypothesis that there is no interaction between sex and species in the mean hemolymph alanine concentration.
ASSIGNMENT No.2
Total Marks: 100
Pass Marks: 40
Q.1. a)Discuss various measures of central tendency and dispersion. Which
ones are most commonly used and why?(10)
b) Data below gives average weekly milk yield (Liters) of a herd of fifty
cows.(10)
13.2 / 11.1 / 9.6 / 17.9 / 15.5 / 6.1 / 16.3 / 19.5 / 10.8 / 19.812.6 / 21.3 / 9.1 / 17.6 / 12.7 / 23.5 / 20.0 / 13.7 / 12.1 / 18.0
16.2 / 16.8 / 14.7 / 14.7 / 18.3 / 13.9 / 25.9 / 10.7 / 15.2 / 16.5
14.3 / 17.1 / 16.9 / 18.8 / 10.4 / 14.6 / 26.2 / 12.5 / 25.9 / 15.9
13.4 / 23.4 / 19.1 / 14.3 / 13.4 / 23.2 / 24.1 / 13.2 / 10.5 / 19.8
i)Arrange the data in seven classes and make a frequency distribution, cumulativefrequencydistribution and a histogram.
ii)Using frequency data compute mean, variance, standard deviation from this data.
iii)If this data comes as random sample from a large population then calculate standard error ofmean and interpret the result assuming that the population of milk yields is normally distributed.
Q.2.a)Write down properties of normal distribution. Also discuss some good
propertiesofestimators which are used in statistical inference.(10)
b)Draw a normal curve with mean milk yield of 15 liters and standards
deviation of three liters fora population of cows. How much area
under the curve lies under one, two and three standard deviations
around the mean? (Hint: Make use of the standard normal table given
in the book). If a random sample 36 cows is drawn from this
population what is the probability that the sample mean yield lies
between 12 to 17 liters?(10)
Q.3.To test a fish-liver oil for its vitamin D potency, 20 day-old chicks were fed a mash to which was added 1% of oil as the only source of vitamin D: 10 similar chicks were fed the same basic mash, but with the addition of 1% of a standard cod-liver oil known for vitamin D potency. After 8 days the individual weights of chicks in the two groups were taken which are given below: (20)
Standard / 69 / 66 / 71 / 69 / 68 / 71 / 74 / 69 / 73 / 70Unknown / 68 / 69 / 66 / 64 / 67 / 69 / 65 / 71 / 68 / 70
Unknown / 65 / 63 / 66 / 68 / 66 / 72 / 69 / 67 / 66 / 61
i)Find the difference between two means and standard error for this difference assuming that the variances are equal.
ii)Find the difference between two means and standard error for this difference assuming that the variances are not equal.
iii)Using the standard error based on pooled variance test the hypothesis of no difference between mean weights of two groups and draw conclusion.
iv)Calculate a 95% confidence interval for the true difference between two treatments and interpret the Cl.
v)Does the conclusion in (iii) and (iv) coincide with one another?
Q.4.Write down complete procedure for executing a paired t-test. Under what condition do we use this test? (20)
Q.5.Write down complete procedure for testing population means of two independent random sample for large sample sizes(>30) (20)
AIOU-AS-347(18)PPU-15-03-2018-200
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