In a poll of 1000 likely voters

Question

 600 say that the united states spends too little on fighting hunger at home. Find 90% confidence interval for the true proportion of voters who feel this way.

Answer 1

The formula for the confidence interval of a proportion is

p^{^} - E < p < p^{^} + E

E = z_α/2 √(p^{^}q^{^}/n)

 

x is the number of successes

n is the total sample size

p^{^} is the sample proportion x/n

q^{^} is 1-p^{^}

z_α/2 is the critical z-value for 90% confidence

 

Based on the data given,

x = 600

n = 1000

p^{^} = 600/1000 = 0.6

q^{^} = 1-0.6 = 0.4

According to a z-chart or calculator, z_α/2 for 90% confidence is 1.645

 

Plug the values in, and use your calculator to find the answer.