In: Statistics and Probability
Nine hundred registered voters are surveyed before a presidential election. Four hundred and eightysix say they will vote for candidate X. Construct a 95% confidence interval for the proportion of registered voters who will vote for candidate X.
Solution :
Given that,
n = 900
x = 480
Point estimate = sample proportion = = x / n = 480/900=0.533
1 - = 1- 0.533 =0.467
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 ( Using z table )
Margin of error = E = Z / 2 * ((( * (1 - )) / n)
= 1.96 (((0.533*0.467) /900 )
E = 0.0326
A 95% confidence interval for population proportion p is ,
- E < p < + E
0.533-0.0326 < p <0.533+ 0.0326
0.5004< p < 0.5656
The 95% confidence interval for the population proportion p is : 0.5004, 0.5656