Eric Garcetti, the mayor of Los Angeles, wants to estimate the
percentage of all residents in
favor of lifting the safer-at-home order and returning to normal
life. He wants to provide a margin of
error of no more than 1.8% with 99% confidence. How many residents
should he sample to achieve this?
Solution :
Given that,
= 0.5
1 - = 1 - 0.5 = 0.5
margin of error = E = 1.8% = 0.018
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 / 0.018)2 * 0.5 * 0.5
=5120.19
Sample size = 5120
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