Question

4. Researchers claim that more than 10% of all football helmets have man- ufacturing defects that could cause injury to the player. A sample of 200 helmets revealed that 24 helmets contained such faults. Do we have significant evidence in favor of the researcher’s declaration? Calculate the p − value and make a decision with α = 5%.

A) p − value=0.3472. At α = 5%, the evidence in favor of the re- searcher’s declaration is significant.

B) p − value = 0.3472. At α = 5%, the evidence in favor of the re- searcher’s declaration is not significant.

C) p − value = 0.1736. At α = 5%, the evidence in favor of the re- searcher’s declaration is not significant.

D) p − value = 0.192. At α = 5%, the evidence in favor of the re- searcher’s declaration is not significant.

E) p − value = 0.1736. At α = 5%, the evidence in favor of the researcher’s declaration is significant.

Answer 1

The statistical software output for this problem is :

One sample proportion summary hypothesis test:
p : Proportion of successes
H₀ : p = 0.1
H_A : p > 0.1

Hypothesis test results:

Proportion	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
p	24	200	0.12	0.021213203	0.94280904	0.1736

P-value = 0.1736

E) p − value = 0.1736. At α = 5%, the evidence in favor of the researcher’s declaration is significant.