Question

A newsgroup is interested in constructing a 90% confidence interval for the proportion of all americans who are in favor of a new green initiative. Of the 560 randomly selected Americans surveyed, 392 were in favor of the initiative.

a. With 90% confidence the proportion of all Americans who favor the new green initiative is between ___ and ___.

Answer 1

Solution :

Given that,

n = 560

x = 392

Point estimate = sample proportion = = x / n = 392/560 = 0.700

1 - = 1-0.700 = 0.300

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

Z/2 = Z_{0.05 = 1.645}

Z/2 = 1.645  

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

= 1.645 * ((0.700*(0.300) /560 )

= 0.032

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.700 -0.032< p < 0.700+0.032

(0.668 , 0.732 )

The 90% confidence the proportion is between 0.668 and 0.732