In: Statistics and Probability
A hat contains 10,000 balls. A random sample of 100 balls is selected from the hat. 17 of the selected balls are red, 27 are green and 56 are black. Construct a 95% confidence interval estimate for the percentage of green balls in the hat.
Solution :
Given that,
n = 100
x = 27
Point estimate = sample proportion = = x / n = 27 / 100 = 0.270
1 - = 1 - 0.270 = 0.730
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.96 * (((0.270 * 0.730) / 100)
= 0.087
A 95% confidence interval for population proportion p is ,
- E < p < + E
0.270 - 0.087 < p < 0.270 + 0.087
0.183 < p < 0.357
a 95% confidence interval estimate for the percentage of green balls in the hat is : 18.3% to 35.7%