A civil engineer plans to investigate 90 randomly selected sections of underground gas piping for minor...

A civil engineer plans to investigate 90 randomly selected sections of underground gas piping for minor cracks; these cracks could be of concern in the future. However, due to time constraints, the engineer could not inspect 22 of the initially selected pipes. Of those inspected, it is found that 12 possess minor cracks. Produce a 99% confidence interval for the proportion of pipes with minor cracks.

Solutions

Expert Solution

Solution :

n = 90

x = 12

Point estimate = sample proportion = = x / n = 12/ 90 = 0.133

1 - = 1- 0.133 = 0.867

At 99% confidence level

= 1-0.99% =1-0.99 =0.01

/2 =0.01/ 2= 0.005

Z/2 = Z0.005 = 2.576

Z/2 = 2.576

Margin of error = E = Z / 2 * $\sqrt$ (( * (1 - )) / n)

= 2.576 * ( $\sqrt$ (0.133*(0.867) / 90)

= 0.092

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.133 -0.041 < p < 0.133 +0.041

0.041 < p < 0.226

( 0.041 , 0.226 )

orchestra answered 1 year ago

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