Consider a random sample X1,...,X, of voters who either voted for Candidate A (“X; = 1") or for Candidate B (“X; = 0"). Denote the probability of voting for Candidate A by p. We wish to test Họ :p2...

Extracted text: Consider a random sample X1,...,X, of voters who either voted for Candidate A (“X; = 1") or for Candidate B (“X; = 0"). Denote the probability of voting for Candidate A by p. We wish to test Họ :p2 0.5 vs. H1 : p< 0.5.="" (i.e.="" the="" hypothesis="" that="" candidate="" a="" will="" not="" loose="" the="" election).="" (1)="" consider="" a="" test="" of="" the="" above="" hypothesis="" of="" the="" form="" i="1" for="" some="" integer="" c.="" calculate="" the="" power="" of="" this="" test="" and="" show="" that="" it="" is="" a="" decreasing="" function="" of="" p="" for="" any="" c="" e="" {0,="" ...,n="" –="" 1}.="" (2)="" suppose="" that="" n="20." find="" c="" so="" that="" v="" in="" (1)="" is="" a="" test="" at="" level="" 10%="" with="" the="" largest="" possible="" power="" (from="" among="" the="" tests="" of="" the="" same="" form="" at="" level="" 10%).="" what="" is="" the="" size="" of="" your="" test?="" use="" that="" the="" cdf="" of="" the="" binomial="" distribution="" with="" size="" 20="" and="" success="" probability="" 0.5="" evaluated="" at="" r="0,...," 20="" equals="" (rounded="" to="" 3="" decimal="" places)="" round="" (pbinom(0:20,="" size="20,p=0.5),3)" ##="" [1]="" 0.000="" 0.000="" 0.000="" 0.001="" 0.006="" 0.021="" 0.058="" 0.132="" 0.252="" 0.412="" 0.588="" 0.748="" ##="" [13]="" 0.868="" 0.942="" 0.979="" 0.994="" 0.999="" 1.000="" 1.000="" 1.000="" 1.000="" (3)="" suppose="" that="" 5="" voters="" voted="" for="" candidate="" a="" and="" 15="" for="" candidate="" b.="" is="" it="" safe="" to="" conclude="" using="" the="" test="" you="" derived="" in="" part="" (2)="" at="" level="" 10%="" that="" candidate="" a="" will="" loose="" the="">