A random sample of 50 suspension helmets used by motorcycle riders and automobile race-car drivers was...

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Statistics

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 â‰ 0.3 with Î± =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 Î²-error at 0.1 (or thepower at 90%)?

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3.6 Ratings (619 Votes)

aTest the hypotheses H0 p 03 versus H1 p 03 with 005 using the normal approximation p 1850 036 n 50 p 03 The test statistic z p pp1pn 036 030310350 093 bFind the Pvalue for See Answer

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