Question

"Large Sample Proportion Problem. Surveys were conducted in multiple countries and respondents were asked if they felt political news was reported fairly. The data for the United States is that out of 1,000 sampled, 470 indicated yes, they felt political news was reported fairly. Suppose we want to construct a 95% confidence interval. What is the standard error for the confidence interval?"

Answer 1

Answer: 0.0158

Step-by-step explanation:

Given : The data for the United States is that out of 1,000 sampled, 470 indicated yes, they felt political news was reported fairly.

According to the given information we have,

Sample size : n= 1000

Sample proportion: $\hat{p}=\dfrac{470}{1000}=0.47$

The standard error for proportion is given by :-

$S.E.=\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$S.E.=\sqrt{\dfrac{0.47(1-0.47)}{1000}}$

$S.E.=\sqrt{0.0002491}$

$S.E.=0.0157829021412\approx0.0158$

[Rounded to the nearest four decimal places.]

Hence, the standard error for the confidence interval = 0.0158