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}=(141)/(200)=0.705`

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

`z_{(\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