Answer: [tex](0.273,\ 0.783)[/tex]
Step-by-step explanation:
Given : Total number of students who are asked to complete a survey anonymously : n= 240
Number of students
The proportion report that they have experienced bullying =54
Then , the proportion that students have experienced bullying =[tex]p=\dfrac{54}{240}=0.225[/tex]
Significance interval : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
The confidence interval for the true proportion is given by :-
[tex]p\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}\\\\=0.225\pm (1.96)\sqrt{\dfrac{(0.225)(1-0.225)}{240}}\\\\\approx0.225\pm0.0528\\\\=(0.255-0.528,\ 0.255+0.528)\\\\=(0.273,\ 0.783)[/tex]
