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)

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.