 ## 1.5 Calculate probabilities using R for normal and Log normal distributions.

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# Unit DS02: Statistical Inference

QUALIFI Level 7 Diploma in Data Science

Unit code: L/618/4971 RQF
level: 7

Aim
This unit provides learners with an in-depth understanding of statistical distribution and hypothesis testing. Statistical distributions include Binomial, Poisson, Normal, Log Normal, Exponential, T, F and Chi Square.

Parametric and non-parametric tests used in research problems are covered in this unit. The unit will help learners to formulate research hypotheses, select appropriate tests of hypothesis, write mainly R programs to perform hypothesis testing and to draw inferences using the output generated. Learners will also study planned experiments as part of the unit.

Learning Outcomes and Assessment Criteria

 Learning Outcomes. When awarded credit for this unit, a learner will be able to: Assessment Criteria. Assessment of this learning outcome will require a learner to demonstrate that they can: 1. Evaluate standard discrete and standard continuous distributions. 1.1  Analyse the statistical distribution of a discrete random variable. 1.2  Calculate probabilities using R for Binomial and Poisson Distribution. 1.3  Fit Binomial and Poisson distributions to observed data 1.4  Evaluate the properties of Normal and Log Normal distributions. 1.5  Calculate probabilities using R for normal and Log normal distributions. 1.6  Fit normal, Log normal and exponential distributions to observed data. 1.7  Evaluate the concept of sampling distribution (t, F and Chi Square). 2. Formulate research hypotheses and perform hypothesis testing. 2.1  Write R and Python programmes that evaluate appropriate hypothesis tests 2.2  Draw statistical inference using output in R 2.3  Translate research problems into statistical hypotheses 2.4  Assess the most appropriate statistical test for a hypothesis 3. Analyse the concept of variance (ANOVA) and an select an appropriate ANOVA or ANCOVA model. 3.1  Define variable, factor and level for a given research problem. 3.2  Evaluate the sources of variation, explained variation and unexplained variation. 3.3  Define a linear model for ANOVA/ANCOVA. 3.4  Confirm the validity of assumption based on definitions and analysis of variation. 3.5  Perform analysis using R and Python programs to confirm validity of assumptions. 3.6  Draw inferences from statistical analysis of the research problem.

Assessment Guidance

To demonstrate all learning outcomes and assessment criteria, each unit should follow the same assessment methodology:

• Formative: Weekly assignments focussing on knowledge and understanding of technical skills using sample data sets over a period of 2 weeks and participation in weekly live classrooms and discussion groups;
• Summative: 1. Formal timed exam testing technical knowledge 2. Component of two individual course projects based on real word data analytics

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