Question

A researcher claims that at least 10% of all football helmets have manufacturing flaws

that could potentially cause injury to the wearer. A sample of 200 helmets revealed that

16 helmets contained such defects. Does this finding support the researcher’s claim?

Answer 1

$H_0: p ≥ 0.10 \\ H_1: p< 0.10 \\ n=200 \\ x = 16 \\ \hat{p} = \frac{16}{200}=0.08$

Let use α=0.05

Test-statistic

$Z = \frac{\hat{p} -p}{\sqrt{\frac{p(1-p)}{n}}} \\ = \frac{0.08-0.1}{\sqrt{\frac{0.1(1-0.1)}{200}}} \\ = -0.9428$

This is a left tailed test.

By using Z table we get p-value = 0.1729

Hence p-value > α

0.1729>0.05

We ccept H₀.

This finding supports the researcher’s claim.