Question

In a random sample of 29 middle schoolers, 10 of them failed. Create a 95% confidence interval for the true proportion of kids who failed.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 10/29=0.345

1 -   = 1-0.345 =0.655

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 (((0.345*0.655) /29 )

= 0.173

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.345-0.173 < p < 0.345+0.173

(0.172 , 0.518)