Answer: [tex](0.1481323,\ 0.2018677)[/tex]
Step-by-step explanation:
The confidence interval for population proportion :
[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex] , where n= sample size, [tex]\hat{p}[/tex] = sample proportion , z*= Critical z-value.
Let p = population proportion of successes.
Given: n= 200 , [tex]\hat{p}=\dfrac{35}{200}=0.175[/tex]
Critical z value for 95% confidence = 1.96
The 95% confidence interval for a population proportion is:
[tex]0.175\pm (1.96)\sqrt{\dfrac{(0.175)(1-0.175)}{200}}\\\\=\ 0.175\pm (1.96)\sqrt{0.000721875}\\\\= 0.175\pm (1.96)(0.0268677)\\\\=(0.175-0.0268677,0.175+0.0268677)\\\\= (0.1481323,\ 0.2018677)[/tex]
Required confidence interval: [tex](0.1481323,\ 0.2018677)[/tex]
