Question

A state's environmental agency worries that a larger percentage of cars may be violating clean air standards. In the past, the percentage of cars that violate clean air standards has been 10%. The agency hopes to check a sample of vehicles in order to estimate that percentage with a margin of error of 1% and with 99% confidence.

How many cars should be sampled? Show your work! Formula(s), substitutions, answer! Round your z or t value to 3 decimal places.

Answer 1

Solution :

Given that,

= 0.10

1 - = 1 - 0.10 = 0.90

margin of error = E = 1% = 0.01

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576 ( Using z table )

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

= (2.576 / 0.01)2 * 0.10 * 0.90

=5972.19

Sample size = 5973