The following course content has been agreed upon by the relevant departments as the introductory course to be taught in the second semester of the First Year Agriculture in all departments.

COURSE ORGANISATION

Lectures:       39 x 1hr

Practicals:     13 x 3hr

Grading:

Continuous assessment:                     40%

Assignments
Practicals
Quizzes

Final Examination:                            60%

One open book 2 hour written paper.

COURSE TEXT BOOKS:

Until such times when textbooks are available at affordable prices, the text allowed in the examination room will be: “Introduction to Biometry” by Sr. Jane Canhao. Other texts are
available and students may buy them for reference if they so wish, but should not be brought into the examination room.

COURSE CONTENT:

1. Introduction

•  The objectives of statistics
•  Delinitions: Populations, samples, continuous and discrete variables, continuous and discrete data, etc.
•  The objectives of simple random sampling and the use of random number tables.

• Graphical Methods: Describing shapes of population distributions with histograms, bar graphs, stem and  leaf plots, and trends  with scatter  plots; Identifying outlying observations using the plots
• Numerical Methods: Estimation of the center and the dispersion of population distributions using the measures of central tendency and dispersion, respectively
• Graphical and Numerical Methods of describing data using MINITAB.

• Definitions: Classical interpretation, relative frequency  concept, statistical experiment, discrete and continuous sample spaces, events, probabilities of simple events.
• Basic relations of events. Complement of an event, mutually  exclusive events, union of events, intersection of events.
• Probability laws: Calculation of probabilities of compound events
• Random variables General definitions of discrete and continuous random and definitions at: sample spaces.
• Probability distributions for discrete random variable:
• General definition of a discrete sample space; Calculation of probabilities, Sampling with or without replacement, Special discrete distributions (Binomial, Poisson)
• Probability distribution for continuous random variables:
• General definition of a continuous sample space; Probabilities as areas under the probability density function. The normal distribution (empirical rule, graphical methods of checking normality, the z-score transformation, use of the z -- tables)

• Sampling distribution of the sample mean: Estimation of the population mean (standard error of the sample mean), Small samples (z and l distributions); Large samples (central limit theorem); Probability calculations
• Interval Estimation at the Populalion Mean; z and t intervals; Sample size required to obtain a specified precision
• Hypothesis test for the population mean: Definition (or the null and research hypotheses, test statistic (z, t), rejection regions and decision rule, type 1 and type 2 errors
•  Inferences using MINITAB

    5.1 Independent Samples:

• Sampling distribution of the differences between sample means
• Interval estimation at the difference between population means; sample size required to ob-tain a specified precision
• Hypotheses test for the difference between population means
• Non parametric alternative; Wilcoxon Rank Sum Test

•  Sampling distribution
•  Interval Estimation; Sample size required to obtain a specified precision
•  Hypotheses testing
•  Non parametric alternative: Wilcoxon Signed-Rank Test
•  Inference using MINITAB

•  Sampling distribution of a sample variance: Point estimation; Use of the Chi Square tables
•  Interval Estimation of a population Variance (Chi square - interval)
•  Hypotheses Test for a population variance (Chi square test)
•  Comparing two population variances: Use of the F tables; F-test.

• Sampling distribution of a sample proportion: Point estimation (standard error of estimate); normal approximation to the binomial distribution
• Interval estimation of a binomial proportion: Sample size required to obtain specified precision
• Hypotheses test for binomial proportions

•  Sampling distribution of the difference between sample proportions
•  Interval estimation of the difference between binomial proportions
•  Hypotheses test about the difference between binomial proportions

•  The fit of the multinomial and Poisson distributions

•  Test for independence of two variables

• Simple linear regression model and its applications
• Graphical and numerical methods of checking the adequacy of the model: Scatter plots and correlations
• Estimation of the model parameters: Least squares method
• Checking the model error assumptions
• Inference about the model parameters: Interval estimation (t) and hypotheses testing (t, F tests)
• Inferences concerning the mean response and the response curve.
• Transformations to achieve linearity, normality and constant variance.
• Use of MINITAB for parameter estimations.