determine the average savings balance on a particular day. error of tolerance is 50. what is the minimum number of accounts he must sample to construct a 95% confidence interval. the standard deviation is 350
To determine the minimum number of accounts that need to be sampled to construct a 95% confidence interval with an error tolerance of 50, we need to use the formula for sample size calculation.
The formula for sample size calculation for means is given by:
n = (Z * σ / E)^2
Where:
n = sample size needed
Z = Z-score for the desired confidence level (95% confidence level corresponds to a Z-score of approximately 1.96)
σ = standard deviation of the population
E = margin of error or error tolerance
Plugging in the given values, we have:
n = (1.96 * 350 / 50)^2
Calculating the value inside the brackets:
n = (1.96 * 350 / 50)^2
n = (686 / 50)^2
n = (13.72)^2
n ≈ 188.24
Since we can't have a fraction of a sample, we need to round up to the nearest whole number. Therefore, the minimum number of accounts that must be sampled to construct a 95% confidence interval with an error tolerance of 50 is 189 accounts.