Question

Pacific Brant ~ Air traffic affects the migratory flights of a species of small goose called the Pacific Brant. When an aircraft flies over a flock of birds, it is called overflight. To estimate the proportion of overflights that affect Pacific Brant’s migratory flights, Wayne takes a random sample of 494 overflights and finds that 349 of them affected Pacific Brant’s migratory flights.

Using this data, Wayne wants to estimate the actual proportion of Pacific Brant’s migratory flights that are affected by overflights.

To calculate the required sample size, what value of p*. should we use in the formula below to calculate a 90% confidence interval within 4.13 percentage points? Give your answer to 4 decimal places.

n=p*(1−p*)(z*ME)2

Answer 1

Solution :

Given that,

= X / n = 0.7065

1 - = 0.2935  

margin of error = E = 0.0413

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= (1.645 / 0.0413)2 * 0.7065 * 0.2935

= 328.9667

sample size = 329