A company developing scanners to search for hidden weapons at airports ...

A company developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner. The company made this decision based on a P-value of 0.03. Explain the meaning of the P-value in this context 

Two students studying BES I are worried about the failure rate. 

a) The first has no idea what the failure rate is so takes a random sample of 100 students of whom 28 failed. Based on the sample evidence, calculate the 95% confidence interval and interpret it. Would this student conclude that the failure rate is 20%? 

b) The second student has a prior belief that the fail rate is 20%. Set up and test the appropriate hypotheses, at a(alpha) =0.05 using the same sample as above. Would this student conclude that the fail rate is 20%? c) In your own words, compare your answers to part (a) and (b) above - do they reach the same conclusion? Why or why not?