Question

In 2006,the General Social Survey (which is conducted uses a method similar to simple random sampling) included a question that asked, "Do you see yourself as someone who is sociable?" For this question, 470 people said that they definitely did out of 1514 randomly selected people. What is the 95% confidence interval for the proportion of all Americans who believe that believe that they are sociable?
A.(0.2563, 0.3645)
B.(0.2804, 0.3404)
C.(0.2871, 0.3337)
D.Assumptions are not met. Can not make confidence interval.

Answer 1

Answer:

Assumptions are not met. Can not make confidence interval.

Step-by-step explanation:

In the General Social Survey, sample size is 1514.

The proportion of those who see themselves social is $\frac{470}{1514}$ ≈ 0.31

To give an 95% confidence interval, we should be able to calculate margin of error of the sample mean, which is given by the formula

M±$z*\frac{s}{\sqrt{N} }$  where M is the mean of the sample (in the General Social Survey it is 0.31), z is z-score for the 95% confidence level(approx. 1.94), s is the standard deviation of the sample, N is the size of the sample(in this example it is 1514).

Since we don't know the standard deviation of the sample, we cannot give a confidence interval.