Question

In a random sample of 75 individuals, it was found that 52 of them prefer coffee to tea. What is the margin of error for the true proportion of all individuals who prefer coffee?
a. 0.006

b. 0.053

c. 0.084

d. 0.106

Answer 1

that will depend on your significant figure ....

Answer 2

but in general:\[z=\frac{\hat p-p}{\sqrt{pq/n}}\]
\[z=\frac{Error}{\sqrt{pq/n}}\]
\[\pm z\sqrt{pq/n}=Error\]
so teh margin of error is going to depend on your significant figure for z_alpha

Answer 3

what is a significant figure? that was all the information the question gave :/

Answer 4

its the area that is outside of a confidence interval.

a 90% confidence interval has a significant figure of (100-90)/2 = 5%
a 95% confidence interval has a significant figure of (100-95)/2 = 2.5%
a 99% confidence interval has a significant figure of (100-99)/2 = 0.5%

these are the most common, the smaller the significant figure, the more likely your interval contains the true population parameter

Answer 5

52/75 is what the sample gives us as a comparison of the true population proportion.

therefore, we want to know how far off this sample size may be from the actual population parameter. it could be that this result is simply a by chance outcome and nowhere near the population stuff. how sure do we want to be? the wider we make our confidence interval, the more sure we can be that it contains the actual population parameter: