Question

(3) What is the interpretation of a 95% confidence level? (4) A bank wishes to estimate the mean credit card balance owed by its customers. The population standard deviation is $500. If a 95% confidence desired, how many customers should be sampled? interval is used and an interval of $100 is

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Answer 1

(3)

A 95% confidence interval means that we are 95% confident that the value of the true population parameter lies within the specified interval (a,b)

We are provided a sample statistic and on basic on that sample we have to make some statement about the population parameter. The 95% confidence interval provides the range of values which we can say with 95% confidence that the true population parameter must lie within.

(4)

The following information has been provided:

$\alpha = 0.05, E = 100, \sigma = 500$

The critical value for the significance level α=0.05 is zc​=1.96. The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:

$n \ge \left( \frac{z_c \sigma}{E}\right)^2 = \left(\frac{ 1.96 \times 500}{ 100 }\right)^2 = 96.04$

Therefore, the sample size needed to satisfy the condition n≥96.04, and it must be an integer number, we conclude that the minimum required sample size is n = 97

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