Answer:
0.077 to 0.24
Step-by-step explanation:
[tex]P=\frac{12}{75}=0.16[/tex]
confidence level =95%=0.95
significance level =1-confidence level =1 -0.95= 0.05
[tex]z_\frac{\alpha }{2}=z_\frac{0.05}{2}=1.96[/tex] from the z table
standard error of P [tex]SE=\sqrt{\frac{P\times \left ( 1-P \right )}{n}}[/tex]
[tex]\sqrt{\frac{0.16\times 0.84}{75}}[/tex] as n=75 given
=0.0423
[tex]E=z_\frac{\alpha }{2}\times\sqrt\frac{P\times \left ( 1-P \right )}{n}[/tex]
=1.96×0.0423=0.0289
now confidence interval is given by (0.16-0.0289 ,0.16+0.0289)
=(0.077,0.24)
