Question

Suppose it is desired to estimate the average time a customer spends in a particular store to within 5 minutes with 99% confidence. It is estimated that the range of the times a customer spends in the store is 90 minutes. How large a sample should be taken to get the desired interval? Right-click the link to use this Z table

Answer 1

We know the standard deviation is approx. 1/4 of the range. So we have

estimated standard deviation = = 90/4 =22.5

The following information has been provided: (1)Margin of Error E = 5 (2)Level of significance α=0.01 (3)Population Standard deviation σ =22.5 The critical value for the significance level α=0.01 is Zc =2.5758. This can be found by using either Excel or by using the normal probability table. The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error: Therefore, the sample size needed to satisfy the condition is n ≥ 134.3567, and it must be an integer number, we conclude that the minimum required sample size is

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