Question

A bank sampled its customers to determine the proportion of customers who use their debit card at least once each month. A sample of 50 customers found that only 12 use their debit card monthly. Find a 99% confidence interval for the proportion of customers who use their debit card monthly.

Answer 1

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

$p-z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} }$

$p=\frac{x}{n}$

$p=\frac{12}{50}$

$p=0.24$

$q=1-p=1-0.24=0.76$

$\frac{\alpha }{2} =\frac{\0.01 }{2}=0.005$

$p-z_{\frac{\alpha }{2}} \sqrt{\frac{pq}{n} }$

$0.24-z_{0.005} \sqrt{\frac{0.24*0.76}{50} }$

$0.24-2.58(0.0604)$

$0.24-0.155832$

By rounding to three decimal places we get,

$0.084$

The 99% confidence interval for the proportion of customers who use debit card monthly is (0.084,0.396).