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 for the average savings balance with an error tolerance of 50, you'll need to use the formula for sample size calculation in hypothesis testing.
The formula for sample size calculation is:
n = (Z * σ / E)²
Where:
n = sample size
Z = Z-score (corresponding to the desired confidence level)
σ = standard deviation
E = margin of error
In this case, the desired confidence level is 95%, so Z corresponds to a 95% confidence level. The Z-score value for a 95% confidence level is approximately 1.96. The standard deviation (σ) is given as 350, and the margin of error (E) is 50.
Substituting the known values into the formula, we get:
n = (1.96 * 350 / 50)²
n = (1.96 * 7)²
n = 13.72²
n ≈ 188
Therefore, the minimum number of accounts that need to be sampled to construct a 95% confidence interval with an error tolerance of 50 is approximately 188 accounts.