Question

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test.

H 0 : p equals 0.61 versus Upper H 1 : p less than 0.61 H0: p=0.61 versus H1: p<0.61

n equals 150 comma x equals 87 comma alpha equals 0.1n=150, x=87, α=0.1

what is the P value?

Answer 1

• Here X is random variable,
• Here X follows normal distribution with mean p and standard deviation =p(1-p)/n
• X~Normal(0.61,0.61*(1-0.61)/150)
• HYPOTHESIS TO BE TESTED
• H0: p=0.61 versus H1: p<0.61
• TEST STATISTICS IS GIVEN BY
• 
• the estimated proportion is given by
• P^=87/150=0.58
• now by substituting the appropriate values
• =-0.75330
• P VALUE
• The p value is given by
• P(X<-0.75330)=1-P(X<0.75330)
• =1-0.77337(i.e the p value associated with the z value in the normal table)
• =0.22663
• CONCLUSION
• The p value obtained is greater than 1% significant level .
• Hence we do not have enough evidence to reject the null hypothesis
• Hence we conclude that p=0.61