Question

A survey of 1383 U.S. adults is taken to measure support for increasing federal funding for research on wind, solar, and hydrogen technology.

a) Suppose the sample finds 979 people who would support the increase in funding. Construct and interpret a 90% confidence interval for the proportion of all Americans that would support the funding. (assume all checks are met)

b) Currently politicians claim that between 60% and 75% of Americans would support such funding. Find the minimum sample size needed to estimate the population proportion at the 99% confidence level in order to ensure that the estimate is accurate to within 4% of the population proportion.

Answer 1

Let x be the the number of people who would support the increase in funding.

a) Given : x = 979 , n = 1383

Therefore = x/n = 979 / 1383 = 0.7079

confidence level = 0.90

Therefore α = 1 - 0.90 = 0.1 , 1 - (α/2) = 0.95

So we have to find z score corresponding to area 0.9500 on z score table

So z = 1.645

Confidence interval is given by,

=

=

0.6878 and 0.7280

We are 90% confident that the proportion of all Americans that would support the funding is between ( 68.78% and 72.80% )

b) Given : Lower bound = 0.60 and Upper bound = 0.75

Therefore = =

= 0.675

confidence level = 0.99 and E = 0.04

Therefore α = 1 - 0.99 = 0.01 , 1 - (α/2) = 0.995

So we have to find z score corresponding to area 0.9950 on z score table

So z = 2.575

n =  

=

= 909.1208

n ~ 910

The minimum sample size needed to estimate the population proportion is 910