Use the given information to find the minimum sample size required to estimate an unknown population mean u. How many
adults must be randomly selected to estimate the mean FICO (credit rating)score of working adults in a country? We want 95% confidence that the
sample mean is within 5 points of the
population mean, and the population standard deviation is 65.
n = (1.96* 65/5)^2
n = (109.85/5)^2
n = 483
To find the minimum sample size required to estimate an unknown population mean with a certain level of confidence and margin of error, we can use the formula:
n = (Z^2 * σ^2) / E^2
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (in this case, a 95% confidence level corresponds to a Z-score of approximately 1.96)
σ = population standard deviation
E = margin of error
In this case, the margin of error (E) is given as 5, and the population standard deviation (σ) is given as 65. Plugging these values into the formula, we get:
n = (1.96^2 * 65^2) / 5^2
n = (3.8416 * 4225) / 25
n = 15677.6 / 25
n = 627.104
Rounding up to the nearest whole number, we find that a minimum sample size of 628 adults must be randomly selected to estimate the mean FICO score of working adults in the country with a 95% confidence level and a margin of error of 5 points.