Can someone help me with this problem? I\'m not understanding type I and II erro

Question

Can someone help me with this problem? I'm not understanding type I and II error. In November head injuries, bicycle be able to withstand impact without cracking. 2000 manufacturers recalled more than 243,000 bicycle helmets because tested helmets failed government impact tests. One way test helmets drop them from a fixed height onto a hard surface. A new helmet design has just been introduced. The new helmet is thought to be more stylish than the old helmet, but consumer groups are worried that it may not provide adequate protection. Helmets made using the older design typically only crack 14% of the time. Describe, in the context of this scenario, the meaning of a type I and a type II error.

Explanation / Answer

In this Problem

Null Hypothesis is that failure rate of new stylish helmet is less than or equal to old type of helmets which is 14%.

Alternative Hypothesis is that failure rate of new stylish helmet is more than the old type of helmets which is 14%.

Type I error means rejecting a null hypothesis even if it is true. So, in this case, we will reject the null that means we will say that failure rate of this new stylish helmet is more than the old type of helmets and that means it is more than 14%, but, in reality it is less than or equal to 14%. It may be due to error in sampling or biasness or error in testing cracking height.

Type II error means accepting the null hypothesis even if it is false. So, in this case, we will accept the fact that failure rate of these new introduced helmets are not more than the old type of helmets and equal to 14% only despite in reality having a higher failure rate than 14%. It is the error of sampling or measurement due to which we accept this fact and ignore the reality.

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