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SADC Course in Statistics Confidence intervals using CAST (Session 07)

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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 two sessions with greater confidence calculate and interpret confidence intervals for both a population mean and a population proportion

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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 two sessions can be obtained by working through some of the pages of CAST in Sections 4.3 and 4.4 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

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To put your footer here go to View > Header and Footer 4 Page 3.3: Interpreting a 95% C.I. The reference above is to the third page of Section 4.3: Estimating Parameters The 3 rd page is on interpreting a 95% C.I. Key points emphasised on this page are: The confidence intervals themselves vary over hypothetical repeats of the sampling Only 95% of them (approximately) will include the true population mean.

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To put your footer here go to View > Header and Footer 5 Page 3.4: C.I. of is estimated In the previous two sessions, we always used the standard deviation (s) of the sample in order to compute a 95% C.I. This MUST be done in practice since the true variability of the population is unknown This page of CAST shows the effect of using s instead of while still keeping the value 1.96 as the multiplier for the std. error. This has negligible effect on the 95% confidence interval if the sample size is sufficiently large, say >60

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To put your footer here go to View > Header and Footer 6 Pages 3.5&3.6: Introducing the t-dist n These pages emphasise the need to use a different multiplier (from the t-dist n ) when finding the 95% C.I. based on the sample std. deviation. Page 3.6 demonstrates that 95% of the confidence intervals, over repeat samples, do indeed include the true population mean if using the sample standard deviation and values from the t-distribution.

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To put your footer here go to View > Header and Footer 7 Page 3.7: Further examples This page gives further examples. Read the page and make sure you understand the contents. Next move to Section 4.4: Estimating Parameters

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To put your footer here go to View > Header and Footer 8 Pages 4.2&4.3: Error distributions Page 4.2 introduces the idea of error in an estimated proportion A simulation exercise is used to demonstrate the extent of the error in the sample proportion The next page (4.3) introduces the standard error of an estimated proportion and the use of the normal approximation to the error distribution

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To put your footer here go to View > Header and Footer 9 Pages 4.5&4.6: C.I. for a proportion These pages show how approximate confidence intervals can be found for an estimated proportion the effect of small sample sizes. Further examples are shown on pages 4.4 and 4.7

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To put your footer here go to View > Header and Footer 10 Practical work on CAST follows…

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