Out of a sample of 1200 people, 650 indicated that they werevoting for candidate

Question

Out of a sample of 1200 people, 650 indicated that they werevoting for candidate A. Can we conclude at the .05 level thatA will win the election (receive over 50% of the vote)? Please show work. Thank you! Out of a sample of 1200 people, 650 indicated that they werevoting for candidate A. Can we conclude at the .05 level thatA will win the election (receive over 50% of the vote)? Please show work. Thank you!

Explanation / Answer

Given n=1200, phat=650/1200 = 0.54 =0.05, Z(0.05)=1.645 (check normal table) The test hypothesis is Ho:p0.5 The test statistic is Z=(phat-p)/p*(1-p)/n =(0.54-0.5)/sqrt(0.5*(1-0.5)/1200) =2.77 Since Z=2.77>1.645, we reject Ho. So we can conclude at the .05level that A will win the election (receive over 50% of thevote)

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