Answer: c. 1498
Step-by-step explanation:
Given : Preliminary estimates suggest that about 58% of students at a state university favor implementing an honor code.
i.e. p = 0.58
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
Margin of error = [tex]2.5\5=0.025[/tex]
The formula to find the sample size is given by :-
[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\=(0.58)(1-0.58)(\dfrac{(1.96)}{0.025})^2\\\\=1497.302016\approx1498[/tex]
Hence, the minimum sample size needed = 1498
