Question

A bank wishes to estimate the mean balances owed by customers holding MasterCard. The population standard deviation is estimated to be $500. If a 97 percent confidence interval is used and an interval of $100 is desired, how many cardholders should be sampled?

Answer 1

Answer: 471

Step-by-step explanation:

Given :  The population standard deviation is estimated to be $500.

i.e .  $\sigma=\ 500$

If a 97 percent confidence interval is used and an interval of $100 is desired.

i.e. Margin of error = half of interval

i.e. E= $\dfrac{\ 100}{2}=\ 50$

Significance level : 1-0.97=0.03

Critical value for 97% confidence interval : ${z_{\alpha/2}=z_{0.03/2}=2.17$

Formula for sample size :

$n=(\dfrac{z_{\alpha/2}\ \sigma}{E})^2\\\\=(\dfrac{2.17\times500}{50})^2\\\\=470.89\approx471$

Hence, at-least 471 cardholders should be sampled.