Question

Out of 100 people sampled, 5 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A. Use a 90% confidence level, and give your answers as decimals, to three places.

_____ < p < _______

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 5/100=0.05

1 -   = 1-0.05 =0.95

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.05*0.95) /100 )

= 0.036

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.05-0.036 < p < 0.05+0.036

0.014< p < 0.086