AP Statistics 3.6 P Values Questions
Interpret a p-value as the probability of a result at least as extreme as observed when the null population proportion is assumed true.
- Syllabus
- Effective Fall 2026
- Course
- AP Statistics
Exam points
- calculate one- or two-sided p-values from null-model tails in the direction specified by the alternative
- estimate a p-value from the proportion of simulated null statistics at least as extreme as observed
- interpret a p-value in context as conditional on the null population proportion being true
- use p-value size to assess evidence for the alternative without treating a large value as proof of the null
Covered syllabus points
Question 1
A company manufactures model rockets that require igniters to launch. Once an igniter is used to launch a rocket, the igniter cannot be reused. Sometimes an igniter fails to operate correctly, and the rocket does not launch. The company estimates that the overall failure rate, defined as the percent of all igniters that fail to operate correctly, is 15 percent.
A company engineer develops a new igniter, called the super igniter, with the intent of lowering the failure rate. To test the performance of the super igniters, the engineer uses the following process.
Step 1: One super igniter is selected at random and used in a rocket.
Step 2: If the rocket launches, another super igniter is selected at random and used in a rocket.
Step 2 is repeated until the process stops. The process stops when a super igniter fails to operate correctly or 32 super igniters have successfully launched rockets, whichever comes first. Assume that super igniter failures are independent.
Given that the first 30 super igniters successfully launch rockets, is it reasonable to believe that the failure rate of the super igniters is less than 15 percent? Explain.
Part (c):
The result of the probability calculation in part (a) provides a reason to believe that the failure rate of the super igniters is less than 15 percent. The calculated probability of 0.0076 shows that there is less than a 1 percent chance that 30 or more igniters in a row would not fail if the failure rate was 15 percent. This probability is smaller than conventional significance levels such as α=0.05 or α=0.01, and thus is small enough to make it reasonable to believe that the failure rate of the super igniters is less than 15 percent.
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