Use the given information to find the minimum sample size required to estimate an unknown population mean µ. H?
Use the given information to find the minimum sample size required to estimate an unknown population mean µ.
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 5 points of the population mean, and the population standard deviation is 73.
The minimum sample size required is ___adults (round up to the nearest whole number.)
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So u want the the sample mean be within 5 points of pop mean:
Sample mean /- 5
The 5 is equal to Z * SD (of the sample mean)
= Z * SD (of the pop) / root(n)
so: 5 = Z * SD (of the pop) / root(n)
Find Z from the z-table with probability (0.10/2 : cuz u said 90% conf, ---> so look for z corresponding probablity of (1-0.9)/2 which is 0.05) in the z-table
This Z would be 1.645
So again: 5 = 1.645 x 73/root(n)
root(n) = 24
n = 577
Confidence interval for population mean (Mu) is
sample mean +/- margin of error
Margin of error = Confidence coefficient*Standard error of sample mean
5 = 1.645*73/sqrt n
n = [1.645*73/5]^2 = 577
Therefore, the minimum sample size required is 577 adults to satisfy the indicated conditions.