Question

construct and interpret a 78% confidence interval for the population proportion with n=1200 and x=400

Answer 1

Solution :

Given that,

n = 1200

x = 400

Point estimate = sample proportion = = x / n = 400/1200=0.333

1 -   = 1- 0.333 =0.667

At 78% confidence level the z is ,

Z/2 = Z0.11 = 1.23 ( Using z table )

Margin of error = E = Z/2   * ((( * (1 - )) / n)

= 1.23* (((0.333*0.667) /1200 )

E = 0.0167

A 78% confidence interval for population proportion p is ,

- E < p < + E

0.333- 0.0167< p <0.333 +0.0167

0.3163< p < 0.3497

The 78% confidence interval for the population proportion p is : 0.3163, 0.3497