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7. A random sample of 500 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test. Damage was observed on 168 of these helmets. The Insurance Institute for Highway Safety (IIHS) wishes to determine whether this provides sufficient evidence to claim that more than 30% of suspension helmets will be damaged in high impact crashes. (a) What hypotheses should the IIHS test? (b) What is the observed test statistic for this sample? (c) What is the p-value for this test? (d) Using a significance level of 0.05, should the IIHS clain that more than 30% of suspension helmets will be damaged in high impact crashes? Why or why not?
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