SAJC 2021 H1 Chapter 6 Math Hypothesis Testing Notes_Teacher_V2

2021 SAJC JC1 H1 Maths Chapter 6 : Hypothesis Testing 1 Chapter 6 (Statistics) : Hypothesis Testing tatistic Pre-requisite Knowledge  Sampling Distribution of Means;  Point Estimates Content 6.1 Introduction to Hypothesis Testing 6.2 Terms and definitions 6.2.1 Null Hypothesis and Alternative Hypothesis 6.2.2 Test Statistic 6.2.3 Comparing z-score and critical value; or p-value and level of significance 6.2.4 Formal definitions of p-value and level of significance 6.3 Carrying out a Hypothesis Test (Examples) 6.3.1 Sample size large/small, Population normal, 2 known 6.3.2 Sample size large, Population non-normal, 2 known 6.3.3 Sample size large, Population non-normal, 2 unknown 6.4 Further Examples 6.5 Summary and Checklist Objectives: At the end of the chapter, you should have learnt about the following:  Concepts of null hypothesis (H 0) and alternative hypothesis (H1), test statistic, critical region, critical value, level of significance, and p-value  Formulation of hypotheses and testing for a population mean based on:  a sample from a normal population of known variance  a large sample from any population  1-tailed and 2-tailed tests  Interpretation of the results of a hypothesis test in the context of the question

2021 SAJC JC1 H1 Maths Chapter 6 : Hypothesis Testing 2 6.1 Introduction to Hypothesis Testing Are Coke cans really 330 ml? Are th is type of dumbbells at least 10 kg? Will that slimming centre help customers lose up to 16 pounds in just 4 weeks as promised? Claims abound in advertising and merchandise, as well as elsewhere e.g. social sciences. The most objective way to test whether a claim is valid is to take a (random) sample and measure it. To be specific: In H1 Maths, we measure its sample mean ( x ) and calculate how much it deviates from an assumed population mean ( 0 , which could be based on known facts or some unverified claim). This deviation is expressed in terms of a relative score or probability, which we compare with a predetermined standard to reach a conclusion about whether the claim is valid. This whole procedure is known as hypothesis testing. A statistical hypothesis is a statement, which may or may not be true, concerning one or more population parameters (e.g. mean, variance, proportion). Hypothesis testing is the procedure used to test the validity of this statement based on evidence from random samples drawn from the population. Let us look at some concrete examples: Coke cans are 330ml. Dumbbells are at least 10kg each. We will help you lose up to 16 lbs.

2021 SAJC JC1 H1 Maths Chapter 6 : Hypothesis Testing 3 Example 1a A fizzy drink brand claims that the mean volume of its canned drinks (the volume is normally distributed with standard deviation 10ml) is 330ml. A consumer weighs a random carton of 24 drinks and found that it h