Question

An official of a large national union claims that the fraction of women in the union is not significantly different from 58%. To test this claim a random sample of 400 individuals in the union is taken. Of those 400. 215 are women. Use the p-value to conduct the hypothesis test and use a = 0.05 level of significance. p-value = 0.0446 <0.05: Fail to reject Ho O a. p-value = 0.0446 <0.05; Reject Ho Ob p-value = 0.4714 > 0.05: Fail to reject Ho O c. p-value = 0.4714 > 0.05; Reject Ho O d.

Answer 1

H0:P=0.58

Ha:P$\neq$0.58

p^=x/n=215/400=0.5375

#test statistics

z=(p^-p)/sqrt(p*(1-p)/n)

z=(0.5375-0.58)/sqrt(0.58*(1-0.58)/400)

z=-1.722

P-value=P(|z|>1.722)=2*P(z>1.722)=2*0.0425=0.0850

P-value>$\alpha$=0.05

We failed to reject ho

ie P-value=0.0850>0.05  We failed to reject ho