Question

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).

Answer 1

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)

E = 0.030

A 95% confidence interval proportion p is ,

- E < p < + E

0.167-0.030 < p < 0.167+0.030

0.137< p < 0.197

(0.137 , .197)