In: Math
In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2446 subjects randomly selected from an online group involved with ears. 1083 surveys were returned. Construct a 99% confidence interval for the proportion of returned survey.
Solution :
Given that,
n = 2446
x = 1083
Point estimate = sample proportion = = x / n = 0.443
1 - = 0.557
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 * (((0.443 * 0.557) / 2446)
= 0.026
A 99% confidence interval for population proportion p is ,
- E < p < + E
0.443 - 0.026 < p < 0.443 + 0.026
0.417 < p < 0.469
The 99% confidence interval is : (0.417 , 0.469)