Answer :
Answer: (0.641, 0.719)
Step-by-step explanation:
The confidence interval for population proportion is given by :-
[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
Given : Level of significance : [tex]1-\alpha:0.90[/tex]
Then , significance level : [tex]\alpha: 1-0.90=0.10[/tex]
Since , sample size : [tex]n=380[/tex] , i.e. a large sample.
Critical value : [tex]z_{\alpha/2}=1.645[/tex]
Also, the proportion of individuals plan on voting yes :-
[tex]\hat{p}=\dfrac{260}{380}\approx0.68[/tex]
Then , the confidence interval at the 90% confidence level will be :-
[tex]0.68\pm(1.645)\sqrt{\dfrac{0.68(1-0.68)}{380}}\\\\\approx0.68\pm0.039\\\\=(0.68-0.039, 0.68+0.039=(0.641,\ 0.719) [/tex]
Hence, the confidence interval at the 90% confidence level= (0.641, 0.719)