Therefore a one tailed test 2 ? 3 ݔ for this one

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: (therefore a one tailed test) 2) ࢻ ൌ 3) ݔ ൌ For this one tailed test ܺ counts the number of ‘overs’ because suggests there should be more of these Denote each age by a plus or minus sign, depending on whether it’s above or below the hypothesised median value 23.1; 27.4; 29.2; 25.8; 30.0; 41.2; 31.3; 28.4; 29.5; 19.4 1) Form two opposing hypotheses and 2) Decide on a significance level for the test 3) Calculate a test statistic x 4) Find the p value using the test statistic 5) Either reject or fail to reject the null hypothesis 6) Make a conclusion about the population 44 4) For the p value we require the probability that X is at least as extreme as 6 out of 10 mothers being over the age of 27.5 ܺ~ܤ݅݊ሺ10,0.5ሻ ܲ ܺ ൒ 6 ൌ ? ܲ ܺ ൒ 6 ൌ 0.377 ሺ3݀݌ሻ from Excel This is a one tailed test so we should not double ܲሺܺ ൒ 6ሻ p value ൌ 0.377 ሺ3݀݌ሻ _ _ + _ + 23.1; 27.4; 29.2; 25.8; 30.0; + + + + _ 41.2; 31.3; 28.4; 29.5; 19.4 45
21/11/2018 16 Bar graph showing the probabilities for ܺ~ܤ݅݊ሺ10,0.5ሻ 46 1 ) ܪ : ݉݁݀݅ܽ݊ ൌ 27.5 ܪ : ݉݁݀݅ܽ݊ ൐ 27.5 (so one tailed test) 2) ࢻ ൌ 0.05 3) ݔ ൌ 6 overs ܺ counts the number of ‘overs’ because ܪ suggests there should be more of these 4) For p value we require prob. that X is at least as extreme as 6 out of 10 ܺ~ܤ݅݊ሺ10,0.5ሻ so ܲ ܺ ൒ 6 ൌ 0.377 ሺ3݀݌ሻ from Excel (one tailed test so do not double) p value ൌ 0.377 ሺ3݀݌ሻ 5) p value ൐ ࢻ ሺ0.377 ൐ 0.05ሻ so do not reject H 6) Conclude that we do not have sufficient evidence of an increase in the median age above the 1990 figure of 27.5 years _ _ + _ + 23.1; 27.4; 29.2; 25.8; 30.0; + + + + _ 41.2; 31.3; 28.4; 29.5; 19.4 47 Clearly show all six steps: Summary of how to calculate both test statistic and p value for a Sign Test H 1 : Test statistic p value median m 0 ݔ = no. of + (overs) ܲሺܺ ൒ ݔሻ median m 0 ݔ = no. of (unders) ܲሺܺ ൒ ݔሻ median m 0 ݔ = maximum of (no. of +, no. of ) 2 ൈ ܲሺܺ ൒ ݔሻ H 0 : median m 0 if it’s a two sided test, need to find the probabilities in both tails 48
21/11/2018 17 Useful mnemonic for remembering what conclusion the p value leads us to: ‘if p value is low, the null must go!’ (lower than alpha) 49 Hypothesis testing in one sentence! 50 Scores have been collected in a psychological test as follows. Use a Sign Test to determine if there is evidence at the 10% level of significance that the median has changed from 29 (the median value when the test was last used) 36; 43; 9; 37; 48; 29; 31; 24; 40; 37 1) ܪ : ܪ : 2) ߙ ൌ 3) ݔ ൌ 4) ܲ ܺ ൒ so p value 5) Compare p value to ߙ and then do or do not reject ܪ 6) Conclusion: 51 1) Form two opposing hypotheses and 2) Decide on a significance level for the test 3) Calculate a test statistic x 4) Find the p value using the test statistic 5) Either reject or fail to reject the null hypothesis 6) Make a conclusion about the population Sign Test Example 3
21/11/2018 18 ܺ~ܤ݅݊ ݊′, ݌ ܺ~ܤ݅݊ 9,0.5 ܲ ܺ ൒ 7 ൌ 0.0898 ሺ4݀݌ሻ from Excel p value ൌ 2 ൈ 0.0898 ൎ 0.18 (two tailed test) See ‘Help with Excel #12’ for more detail 52 Scores have been collected in a psychological test as follows.

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