Dr. v. r. bencivenga and dr. stephen donald economics 329 homework question - belief in global warming in a large city a certain (unknown) proportion of adults believe that global warming is a liberal hoax designed to hurt oil companies. you plan to take a survey of n adults to "estimate" this proportion. you want to be able to say that your estimate is within three percentage points (i. e., within 0.03) of the true proportion, with 0.95 probability. what is the smallest sample size that guarantees that you would obtain a satisfactory estimate (an estimate that's within 0.03 of the true proportion, with probability 0.95)? provide an answer using an approximation based on the central limit theorem a. 752 b. 2135 c. 4269 d. 1068

d. 1068

Step-by-step explanation:

Let p be the proportion of adults believe that global warming is a liberal hoax designed to hurt oil companies.

Given : You plan to take a survey of n adults to "estimate" this proportion. You want to be able to say that your estimate is within three percentage points (i.e., within 0.03) of the true proportion, with 0.95 probability.

Margin of error : E= 0.03

We know that the z-value for 95% confidence =

Since the prior proportion of adults believe that global warming is a liberal hoax designed to hurt oil companies.  

We assume p = 0.5

Then by Central Limit Theorem , the required sample size would be :

Simply , we get

 [Rounded to the next whole number.]

Hence, the smallest sample size that guarantees that you would obtain a satisfactory estimate  =1068

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

step-by-step explanation: