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To show they should provide adequate protection against head injuries, bicycle helmets must be
able to withstand government impact tests without cracking more than 10% of the time. A new
helmet design has just been introduced. The new helmet is thought to be more stylish than older
helmets, but consumer groups are worried that it may not pass government impact tests and will
not provide adequate protection.
2000 of the new helmets are randomly sampled and tested. Of these sampled helmets, 210 of
them cracked. Test the hypothesis that the new helmets will crack more than 10% time when
enduring the impact tests. Use .05 as the level of significance.
a) State the null and alternative hypotheses using proper notation.
b) What test are you using?
c) Give the values of the test statistic, and the p-value.
d) Use your p-value to make your decision regarding the null hypothesis.
e) What is your conclusion regarding the whether or not the new helmet cracks more than 10%
the time. Be sure to use the phrase "statistically significant."

Sagot :

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