In: Statistics and Probability
About 27% of US citizens say football is their favorite sport to watch on TV. A random sample of 100 US citizens is obtained. Is the sampling distribution of the sample proportion normally distributed? Why?
Solution
Given that,
p = 0.27
1 - p = 1 - 0.27 = 0.73
n = 100
The sampling distribution of
is approximately normal because,
np
10 and n(1 - p)
10
100 * 0.27 = 27
10 and 100 * 0.73 = 73
10
= p = 0.27
[p
( 1 - p ) / n] =
[(0.27 * 0.73) / 100 ] = 0.0444