1. SADC Course in Statistics Revision using CAST (Session 04)

2. To put your footer here go to View > Header and Footer 2 Learning Objectives By the end of this session, you will be able to explain concepts learnt in the previous session with greater confidence, e.g. what is meant by an estimate of a population parameter, the sampling distribution of an estimate, and the standard error of a sample mean have greater understanding of sampling distributions and standard errors explain the implications of the Central Limit Theorem

3. To put your footer here go to View > Header and Footer 3 Using CAST for SADC: Higher Level Further insight into the concepts introduced in the previous session can be obtained by working through pages of CAST in Section 3.1 Practical work using CAST will therefore form the main activity in this session Here we will just highlight a few of the features that CAST aims to demonstrate, while reviewing concepts already covered.

4. To put your footer here go to View > Header and Footer 4 Page 1: Variability of sample mean Key points emphasised on this page are: The distribution of the sample means is centred on the population mean The distribution of the sample means has lower variability than the distribution of the raw sample data drawn from the population

5. To put your footer here go to View > Header and Footer 5 Page 2: Std. Dev. of sample mean Key points emphasised on this page are: The distribution of the sample means is centred on the population mean whatever the sample size The variability of the sample means decreases as the sample size increases

6. To put your footer here go to View > Header and Footer 6 Page 3: Means from normal pop ns Key points emphasised on this page are: When the population has a normal distribution, the sample mean also has a normal distribution If the population has mean () and standard deviation (), the sample mean has mean and standard deviation /n. Hence we may write ~ N(, 2 /n)

7. To put your footer here go to View > Header and Footer 7 Page 4: Means from non-normal pop ns Key points emphasised on this page are: When the population has a non-normal distribution, the sample mean still has a normal distribution, provided n is large This is because of the Central Limit Theorem: Even if raw data has a non-normal distribution, the sample mean is approximately normally distributed, provided the sample size is large enough.

8. To put your footer here go to View > Header and Footer 8 Page 5: Distribution of the mean Key points emphasised on this page are: How variability in the sample mean, i.e. the precision (or std. error) of the sample mean, can be measured using a single sample This is possible because the standard error of the mean is related to the population standard deviation through the formula s.e.m. = / n.

9. To put your footer here go to View > Header and Footer 9 Page 6: Requirement of independence Key points emphasised on this page are: When statisticians use the term random sample, independence of observations is implied unless dependence is otherwise stated The effects of dependence of observations, e.g. leads to greater variability in the sample means

10. To put your footer here go to View > Header and Footer 10 Checking ideas are understood As you work through Section 3.1 of CAST for SADC: Higher Level, check after each page that you have understood the key points highlighted on slides 4 – 9 of this handout. Ask a resource person for help if any of the ideas are not clear.

11. To put your footer here go to View > Header and Footer 11 Practical work using CAST follows…