In: Math
From a random sample of 100 male students at Hope College, 16 were left-handed. Using the theory-based inference applet, determine a 99% confidence interval for the proportion of all male students at Hope College that are left -handed. Round your answers to 4 decimal places, e.g. "0.7523.
Solution :
Given that,
n = 100
x = 16
= x / n = 16 / 100 =
0.16
1 - = 1 - 0.16 = 0.84
At 99% confidence level the z is ,
= 1 - 99% =
1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 =
2.576
Margin of error = E = Z / 2 *
((
* (1 -
)) / n)
= 2.576 * (((0.16 * 0.84) / 100)
= 0.0944
A 99% confidence interval for population proportion p is ,
- E < P <
+ E
0.16 - 0.0944 < p < 0.16 + 0.0944
0.0656 < p < 0.2256
(0.0656 , 0.2256)