Question

Out of 500 people sampled, 320 preferred Candidate A. Based on this, estimate what proportion of the voting population (p) prefers Candidate A. Use a 90% confidence level, and give your answers as decimals, to three places.

answer ____ < p < answer ____

Answer 1

Solution :

Given that,

n = 500

x = 320

Point estimate = sample proportion = = x / n =320 /500=0.64

1 - = 1-0.64=0.36

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645} ( Using z table )

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

= 1.645 (((0.64*0.36) / 500)

E = 0.035

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.64 -0.035 < p <0.64+ 0.035

0.605< p < 0.675

The 90% confidence interval for the population proportion p is : 0.605< p < 0.675