Question

In a random sample of 200 people, 141 said that they watched educational television. Find the lower limit of the 95% confidence interval of the true proportion of people who watch educational television, rounded to three places after the decimal point.

Answer 1

First, we have that the proportion given is:

$\hat{p}=\frac{141}{200}=0.705$

for a confidence interval with 95% of significance level, we can use the following z value:

$z_{\frac{\alpha}{2}}=1.96$

then, the general expression to find the 95% IC for proportions is:

$(\hat{p}-1.96,\hat{p}+1.96)$

in this case, we have the following:

$(0.705-1.96,0.705+1.96)=(-1.255,2.665)$

therefore, the lower limit of the confidence interval is -1.255