A random sample of 50 suspension helmets used by motorcycleriders and automobile race-car drivers was subjected to an impacttest, and on 18 of these helmets some damage was observed.
(a)Test the hypotheses H0: p = 0.3 versus H1: p ≠0.3 with α =0.05, using the normal approximation.
(b)Find the P-value for this test.
(c)Find a 95% two-sided confidence interval on the trueproportion of helmets of this type that would show damage from thistest. Explain how this confidence interval can be used to test thehypothesis in part (a).
(d)Using the point estimate of p obtained from the preliminarysample of 50 helmets, how many helmets must be tested to be 95%confident in order to keep the associated β-error at 0.1 (or thepower at 90%)?
