A union spokesperson claims that 75% of union members will support a strike if t

Question

A union spokesperson claims that 75% of union members will support a strike if their basic demands are not met. A company negotiator believes the true percentage is lower. The negotiator takes a sample of 125 union members, and finds that 87 say they will strike. 1. a. Is there evidence in support of the negotiators belief if we assume a typeerror of 0.1 using the reiection region approach? o(· 0-1 > o( nz'o.lo; .. 2 b. What sample size is required if the true percentage is 72% with probability

Explanation / Answer

here H0:p=0.75 and

H1:p<0.75 ( this is left one tailed test)

P=x/n=87/125=0.696

SE(P)=sqrt(p(1-p)/n))=sqrt(0.75*(1-0.75))/125)=0.0387

now we use standand normal variate Z=(P-p)/SE(P))=(0.696-0.75)/0.0387=-1.3953

critical region Z<z(0.1)=-1.28

left one tailed critical Z(0.01)=-1.28 is more than calculated z=-1.3953, so we fail to accept H0 i.e. reject H0 and conclude that true percentage is lower

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