Question

In a sample of 150 cars, 18 cars failed a safety inspection. The sampling method had a margin of error of 0.02.

What is the interval estimate for the proportion that would fail in the form (lower limit, upper limit)?


 
(0.07,0.11)

(0.10,0.14)

(0.12,0.16)

(0.13,0.17)

Answer 1

(0.10,0.14)

Explanation:

-Given the sample size is 150 and our proportion is 18.

-We first determine the proportion's probability:

`\hat p=(x)/(n)\\\\=(18)/(150)\\\\=0.12`

-The interval estimate for the proportion is then calculated using the formula:

`CI=\hat p\pm MOE\\\\=0.12\pm 0.02\\\\=[0.10,0.14]`

Hence, the interval estimate is for the proportion (0.10,0.14)