Answer:
(0.084,0.396)
Step-by-step explanation:
The 99% confidence interval for the proportion of customers who use debit card monthly can be constructed as
[tex]p-z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} } <P<p+z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} }[/tex]
[tex]p=\frac{x}{n}[/tex]
[tex]p=\frac{12}{50}[/tex]
[tex]p=0.24[/tex]
[tex]q=1-p=1-0.24=0.76[/tex]
[tex]\frac{\alpha }{2} =\frac{\0.01 }{2}=0.005[/tex]
[tex]p-z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} } <P<p+z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} }[/tex]
[tex]0.24-z_{0.005} \sqrt{\frac{0.24*0.76}{50} } <P<0.24+z_{0.005} \sqrt{\frac{0.24*0.76}{50} }[/tex]
[tex]0.24-2.58(0.0604)<P< 0.24+2.58(0.0604)[/tex]
[tex]0.24-0.155832<P<0.24+0.155832[/tex]
By rounding to three decimal places we get,
[tex]0.084<P<0.396[/tex]
The 99% confidence interval for the proportion of customers who use debit card monthly is (0.084,0.396).
