Question

In: Statistics and Probability

Experts have predicted that approximately 1 in 12 tractor-trailer units will be involved in an accident...

Experts have predicted that approximately 1 in 12 tractor-trailer units will be involved in an accident this year. One reason for this is that 1 in 3 tractor-trailer units has an imminently hazardous mechanical condition, probably related to the braking systems on the vehicle.

1. If you wanted to calculate a 99% confidence interval that is no wider than 0.06, how many tractor-trailers would you need to sample?

Expert Solution

Solution,

Given that,

= 1 - = 0.5

margin of error = E = 0.06

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.576 / 0.06)2 * 0.5 * 0.5

= 460.81

sample size = n = 461

orchestra answered 2 years ago

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