Answer: 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