In: Statistics and Probability
A simple random sample of 600 elements generates a sample proportion P=0.60
a. Provide the 90% confidence interval for the population proportion (to 4 decimals).
b. Provide the 95% confidence interval for the population proportion (to 4 decimals).
Solution :
Given that,
n = 600
Point estimate = sample proportion = = = 0.60
1 - = 1- 0.60 =0.40
At 90% confidence level
= 1 - 90%
= 1 - 0.90 =0.10
/2
= 0.05
Z/2
= Z0.05 = 1.645 ( Using z table )
Margin of error = E Z/2 *(( * (1 - )) / n)
= 1.645 *((0.60*0.40) /600 )
= 0.0329
A 90% confidence interval for population proportion p is ,
- E < p < + E
0.60-0.0329 < p <0.60+ 0.0329
0.5671< p < 0.6329
The 90% confidence interval for the population proportion p is : 0.5671, 0.6329
(B)
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 *((0.60*0.40) /600 )
= 0.0392
A 95% confidence interval for population proportion p is ,
- E < p < + E
0.60-0.0392< p < 0.60+0.0392
0.5608< p < 0.6392
The 95% confidence interval for the population proportion p is : 0.5608, 0.6392