In: Statistics and Probability
Determine confidence intervals for each of the following.
Percent = 67%; sample size = 300, confidence level = 95%
Solution :
Given that,
n = 300
Point estimate = sample proportion = = 67%=0.67
1 - = 1-0.67 =0.33
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 (((0.67*0.33) /300 )
E = 0.092
A 95% confidence interval for population proportion p is ,
- E < p < + E
0.67-0.092 < p < 0.67+0.092
(0.578,0.762)