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? Use α = 0.09. Find the P-value.
Round your answer to four decimal places (e.g. 12.3456).
The proportion of football helmets with flaws

exceed or does not exceed 10% ?
The P-value is _____________?

Answer 1

Solution :

This hypothesis test is a two tailed test .

The null and alternative hypothesis is

H₀ : p 0.10

H_a : p < 0.10

= 0.08

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.08 - 0.10 / [(0.10 * 0.90) / 200]

= -0.943

P-value = 0.1729

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to support the researcher's claim .

The proportion of football helmets with flaws does not exceed 10%