Question

To estimate the true proportion of adult citizens who are in favor of new gun control legislations, a random sample of 120 citizens yielded 50 who were in favor. What is an upper limit of a 90% confidence interval for the proportion of citizens who are in favor of the gun control legislation. Enter your answer with two significant places after the decimal. (For example,0.1254 should be entered as 0.13)

Answer 1

Answer: 0.49

Step-by-step explanation:

Given : To estimate the true proportion of adult citizens who are in favor of new gun control legislations, a random sample of 120 citizens yielded 50 who were in favor.

i.e. n=120

Sample proportion: $\hat{p}=\dfrac{50}{120}=0.417$

Critical value for 90% confidence=$z_{\alpha/2}=1.645$

Upper limit of Confidence interval for population proportion :

$\hat{p}+z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$0.417+(1.645)\sqrt{\dfrac{0.417(1-0.417)}{120}}\\\\\approx0.417+0.074=0.491\approx0.49$

Hence,upper limit of a 90% confidence interval for the proportion of citizens who are in favor of the gun control legislation.= 0.49