A random sample of 70 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 15 of these helmets some damage was observed. (a) Find a 95% two-sided confidence interval on the true proportion of helmets of this type that would show damage from this test. Round your answers to 3 decimal places.

Answer : (0.1183 ≤ p ≤ 0.3103)

Step-by-step explanation:

Solution :

Given that,

a) n = 70

x = 15

Point estimate = sample proportion (p)= x / n = 15 / 70 = 0.2143

1 - p = 1 - 0.2143 = 0.7857

At 95% confidence level

α = 1 - 95%

α =1 - 0.95 =0.05

α/2 = 0.025  

Zα/2 = Z0.025 = 1.960

Margin of error = E = Zα / 2 * √ (( p * (1 - p )) / n)

= 1.96 (√((0.2143 * 0.7857) / 70)

= 0.096

A 95% confidence interval for population proportion p is ,

P - E ≤ p ≤ P + E

0.2143 - 0.096 ≤p ≤ 0.2143 + 0.096

(0.1183 ≤ p ≤ 0.3103)

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