A financial institution wishes to estimate the mean balances owed by its credit card customers. The population standard deviation is estimated to be $300. If a 98 percent confidence interval is used and an interval of ±$75 is desired, how many cardholders should be sampled?
A. 87
B. 629
C. 62
D. 3382
87
To determine the sample size needed, we can use the formula:
n = (Z * σ / E)^2
where:
n = sample size
Z = Z-score corresponding to the desired confidence level
σ = population standard deviation
E = desired margin of error
In this case, the desired confidence level is 98 percent, which corresponds to a Z-score of approximately 2.33 (look up in Z-score table). The population standard deviation is estimated to be $300, and the desired margin of error is ±$75.
Plugging in these values into the formula, we get:
n = (2.33 * 300 / 75)^2
n = (6.99)^2
n ≈ 48.86
Since we can't have a fraction of a cardholder, we need to round up to the nearest whole number. Therefore, the estimated number of cardholders to be sampled is 49.
The closest answer choice among the options provided is C. 62.