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A survey asked people to rate their opinion on the economy in January 2016 and January 2017 on a scale from 1 to 10 where

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A survey asked people to rate their opinion on the economy in January 2016 and January 2017 on a scale from 1 to 10 where 10 meant they were "extremely optimistic", 1 meant they were "extremely pessimistic", and 5 indicated that they were "neutral". Here are the results Respondent 2016 2017 A NNHOD JA OSO We wish to test Ho : /2016 = #2017 V.S. H1 : #2016 # #2017. (Hints: for a sign test or sign-ranked test, if the difference of the pair is zero, you candelete that datum. For example here the rst row has the same rating. You should delete it and the sample size becomes 8.) (a) Calculate the signedrank test statistics T. (b) For this set of ranks, calculate the probability under the null hypothesis that T S 3

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