A team of engineers at the research center of a car manufacturer performs crash tests to determine the proportion of times the cars' airbags fail to operate in a crash. With the airbag system's new modified design, the team expected to reduce the failed proportion to below last year's proportion of 0.08 . They decided to test $$\(\mathrm{H}_{0}: p=0.08\)$$ versus $$\(\mathrm{H}_{a}: p< 0.08\)$$, where $$\(p=\)$$ the proportion of failed airbags during crash tests. If 300 crashes performed in the lab resulted in 18 failures, which of the following is the test statistic for this test?
A.
\(z=\frac{0.06-0.08}{\sqrt{\frac{0.08(1-0.08)}{300}}}\)
B.
\(z=\frac{0.06-0.08}{\sqrt{\frac{0.06(1-0.06)}{300}}}\)
C.
\(z=\frac{0.06-0.08}{\sqrt{300(0.08)(1-0.08)}}\)
D.
\(z=\frac{0.06-0.08}{\sqrt{300(0.06)(1-0.06)}}\)
E.
\(z=\frac{0.06-0.08}{\sqrt{\frac{0.06(1-0.08)}{300}}}\)
Exam No：AP Statistics Problem Set 11 Year：2024 Question No：20
Answer:
A
Knowledge points:
5.5 Sampling Distributions for Sample Proportions
6.4 Setting Up a Test for a Population Proportion
6.5 Interpreting p-Values
Solution:
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