How large a sample should be taken if the population mean is to be estimated with 95% confidence to within $69? The population has a standard deviation of $892. (Round you answer up to the nearest whole number.)
You may need to use the appropriate table in Appendix B to answer this question.
To determine the sample size needed to estimate the population mean with a specified level of confidence, we can use the formula:
n = (Z * σ / E)^2
Where:
n = Sample size
Z = Z-value (corresponding to the desired level of confidence)
σ = Population standard deviation
E = Margin of error
Given that the population standard deviation is $892 and the desired margin of error is $69, we need to find the Z-value for the 95% confidence level.
Looking up the Z-value in Appendix B or using a statistical calculator, we find that the Z-value for a 95% confidence level is approximately 1.96.
Plugging in the values into the formula:
n = (1.96 * 892 / 69)^2
Calculating this equation, we get:
n = (1739.12)^2
n ≈ 3,020,043
Rounding up to the nearest whole number, the sample size required is 3,020,044.