Question

A Huffpost/YouGov poll of 1000 Americans found that 45% believed that there is intelligent life on other planets.

a) Construct a 95% confidence interval for the percentage of all Americans who believe there is intelligent life on other planets.

b) Construct a 99% confidence interval for the percentage of all Americans who believe there is intelligent life on other planets.

c) Would it be plausible to conclude that 40% of Americans believe in intelligent life on other planets?

Answer 1

Answer:

a)

Given,

p = 0.45

sample n = 1000

Here at 95% CI, z value is 1.96

CI = p^ +/- z*sqrt(p^(1-p^)/n)

substitute values

= 0.45 +/- 1.96*sqrt(0.45(1-0.45)/1000)

= 0.45 +/- 0.0308

= (0.4192 , 0.4808)

b)

Here at 99% CI, z value is 2.58

CI = p^ +/- z*sqrt(p^(1-p^)/n)

substitute values

= 0.45 +/- 2.58*sqrt(0.45(1-0.45)/1000)

= 0.45 +/- 0.0406

= (0.4094 , 0.4906)

c)

No, in light of the fact that 0.4 isn't falling inside the limits of either 95% or 99% confidence interval. No, it isn't conceivable that 40% of Americans have confidence in insightful life on other planet.