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: [tex]\hat{p}=\dfrac{50}{120}=0.417[/tex]
Critical value for 90% confidence=[tex]z_{\alpha/2}=1.645[/tex]
Upper limit of Confidence interval for population proportion :
[tex]\hat{p}+z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]0.417+(1.645)\sqrt{\dfrac{0.417(1-0.417)}{120}}\\\\\approx0.417+0.074=0.491\approx0.49[/tex]
Hence,upper limit of a 90% confidence interval for the proportion of citizens who are in favor of the gun control legislation.= 0.49
