In: Statistics and Probability
A simple random sample of 600 individuals provides 100 Yes responses.
A). What is the point estimate of the proportion of the population that would provide yes responses ( to 3 decimals, if needed)?
B) What is your estimate of the standard error of the proportion (to 4 decimals)?
C).Compute the 95% confidence interval for the population proportion (to 3 decimals).
Solution :
Given that,
n = 600
x = 100
Point estimate = sample proportion = = x / n = 100/600=0.1667
1 - = 1- 0.1667 =0.8333
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 (((0.1667*0.8333) /600 )
= 0.0298
standard error= (0.1667*0.8333) /600 )=0.0152
A 95% confidence interval for population proportion p is ,
- E < p < + E
0.1667-0.0298 < p < 0.1667+0.0298
0.1369< p < 0.1965
The 95% confidence interval for the population proportion p is : 0.1369, 0.1965