Answer: 99% confidence interval would be (0.13,0.26).
Step-by-step explanation:
Since we have given that
Sample size n = 1418
x = 354
So, [tex]\hat{p}=\dfrac{x}{n}=\dfrac{354}{1418}=0.249[/tex]
At 99% level of significance, z = 2.58
So, interval would be
[tex]\hat{p}\pm z\sqrt{\dfrac{p(1-p)}{n}}}\\=0.249\pm 2.58\times \sqrt\dfrac{0.249\times (1-0.249)}{1418}}}\\\\=0.249\pm 0.01148\\\\=(0.249-0.01148,0.249+0.01148)\\\\=(0.13,0.26)[/tex]
Hence, 99% confidence interval would be (0.13,0.26).