# Therefore a one tailed test 2 ࢻ 3 ݔ for this one

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:(therefore aonetailedtest)2)ࢻ ൌ3)ݔ ൌFor this onetailed testܺcounts the number of ‘overs’becausesuggests there should be more of theseDenote each age by a plus orminus sign, depending onwhether it’s above or below thehypothesised median value23.1; 27.4; 29.2; 25.8; 30.0;41.2; 31.3; 28.4; 29.5; 19.41)Form two opposinghypothesesand2)Decide on asignificance levelfor thetest3)Calculate atest statisticx4)Find thepvalueusing the test statistic5)Eitherrejectorfail to rejectthenullhypothesis6)Make aconclusionabout thepopulation444)For thepvalue we require the probability thatXis at least asextreme as 6 out of 10 mothers being over the age of 27.5ܺ~ܤ݅݊ሺ10,0.5ሻܲܺ ൒ 6ൌ ?ܲܺ ൒ 6ൌ 0.377 ሺ3݀݌ሻfrom ExcelThis is aonetailed testso we shouldnotdoubleܲሺܺ ൒ 6ሻpvalueൌ 0.377 ሺ3݀݌ሻ__+_+23.1; 27.4; 29.2; 25.8; 30.0;++++_41.2; 31.3; 28.4; 29.5; 19.445
21/11/201816Bar graph showing the probabilities forܺ~ܤ݅݊ሺ10,0.5ሻ461)ܪ: ݉݁݀݅ܽ݊ ൌ 27.5ܪ: ݉݁݀݅ܽ݊ ൐ 27.5(so onetailed test)2)ࢻ ൌ 0.053)ݔ ൌ 6oversܺcounts the number of ‘overs’ becauseܪsuggests there should bemore of these4)Forpvalue we require prob. thatXis at least as extreme as 6 out of 10ܺ~ܤ݅݊ሺ10,0.5ሻsoܲܺ ൒ 6ൌ 0.377 ሺ3݀݌ሻfrom Excel(onetailed test so do not double)pvalueൌ 0.377 ሺ3݀݌ሻ5)pvalue൐ ࢻ ሺ0.377 ൐ 0.05ሻso do not rejectH6)Conclude that we do not have sufficient evidence of an increase inthe 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; 19.447Clearly show all sixsteps:Summary of how to calculate both test statisticandpvalue for a Sign TestH1:Test statisticpvaluemedianm0ݔ= no. of +(overs)ܲሺܺ ൒ ݔሻmedianm0ݔ= no. of(unders)ܲሺܺ ൒ ݔሻmedianm0ݔ= maximum of (no. of +, no. of)2 ൈ ܲሺܺ ൒ ݔሻH0:medianm0if it’s a twosided test, need to find the probabilities inbothtails48
21/11/201817Useful mnemonic for remembering what conclusion thepvalue leads us to:‘ifpvalue is low, the null must go!’(lower than alpha)49Hypothesis testing in one sentence!50Scores have been collected in a psychological test asfollows. Use a Sign Test to determine if there isevidence at the 10% level of significance that themedian has changed from 29 (the median value whenthe test was last used)36;43;9;37;48;29;31;24;40;371)ܪ:ܪ:2)ߙ ൌ3)ݔ ൌ4)ܲܺ ൒sopvalue5) Comparepvalue toߙand then do or do not rejectܪ6) Conclusion:511)Form two opposinghypothesesand2)Decide on asignificancelevelfor the test3)Calculate atest statisticx4)Find thepvalueusing thetest statistic5)Eitherrejectorfail to rejectthenullhypothesis6)Make aconclusionaboutthe populationSign Test Example 3
21/11/201818ܺ~ܤ݅݊݊′, ݌ܺ~ܤ݅݊9,0.5ܲܺ ൒ 7ൌ 0.0898 ሺ4݀݌ሻfrom Excelpvalueൌ 2 ൈ 0.0898 ൎ 0.18(twotailed test)See ‘Help with Excel #12’ formore detail52Scores have been collected in a psychological test as follows.

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