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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)

Respuesta :

opudodennis

Answer:

(0.10,0.14)

Step-by-step explanation:

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

-We first determine the proportion's probability:

[tex]\hat p=\frac{x}{n}\\\\=\frac{18}{150}\\\\=0.12[/tex]

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

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

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

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