Hypothesis testing KUS objectives BAT find critical regions

Hypothesis testing • KUS objectives BAT find critical regions for hypothesis tests Starter:

Critical values and regions What values will lead you to reject Ho? These are known as the critical region(s) of an Hypothesis Test. The values on the boundary of the critical region(s) are called critical value(s) For eg previously, X~Po(10), if the significance level is set at 5% and the claim is that the rate has reduced (ie a 1 -tail test) So X=4 is the largest value which could be observed and lead you to reject Ho Hence X=4 is the critical value and X≤ 4 is the critical region For eg previously, X~Po(10), if the significance level is set at 20% and the claim is that the rate has changed (ie a 2 -tail test) Hence X=5 is a critical value and X≤ 5 is a critical region Hence X=15 is a critical value and X≥ 15 is a critical region

Significance levels How do you decide what is classed as enough evidence to reject Ho? An hypothesis test is given a significance level, a cut-off point to reject Ho. In the exam you will be told the significance level to use What does the significance level represent? One way of phrasing it is ‘the probability of incorrectly rejecting Ho’ What is the actual significance level of a test? The probability of incorrectly rejecting Ho, for the result you obtained

WB 10 A Physics course includes a multiple choice test. There are 20 questions in the test and each question has 4 possible answers. The staff want to see if the students are doing better than random guessing Form a Hypothesis and find the critical region for a one tailed test if the significance level is 5% 1 -0. 8982= 10. 18% 1 -0. 9591= 4. 09% 1 -0. 9861= 1. 39% 1 -0. 9961= 0. 39% 1 -0. 9991= 0. 09% Ta da!

WB 10 Graphically Physics Mult choice Distribution 0, 2500 0, 2000 0, 1500 0, 1000 0, 0500 0, 0000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Series 1 These probabilities sum to 4. 09% This is the actual significance level

WB 11 An anti-smoking campaign is held in a city. Before the campaign Health workers estimated that 30% of adults smoked cigarettes. After the campaign, a random sample of 15 adults are surveyed to test if the campaign has had any impact on the smokers, positive or negative. Form a Hypothesis and find the critical regions for a Two tailed test if the significance level is 10% 0. 0352= 3. 52% Ta da! 0. 1268= 12. 68% 1 -0. 8688= 13. 12% 1 -0. 9499 5. 01% Ta da! (close enough)

WB 11 Graphically Anti-smoking Distribution 0, 2500 0, 2000 0, 1500 0, 1000 0, 0500 0, 0000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Series 1 These probabilities sum to 8. 53% This is the actual significance level

Practice Ex 105 C

KUS objectives BAT find critical regions for hypothesis tests self-assess One thing learned is – One thing to improve is –

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