Question

The formula below is used to determine the minimum sample size n for a given design, where B is the bound on the error of the estimate. z

α/2×( Standard error of the estimator) ≤B Recall that the standard error of a population mean is n
​

σ , where σ is the population standard deviation, and n is the sample size we are trying to determine. Substituting the standard error into the minimum sample size formula gives us the formula below. z
α/2( n
​σ )≤B of z with an area of 0.025 to its right. Round your answer to two decimal places. z
0.025 = using the value of z
0.025
determined in a previous step, z
0.025=1.96. Round your answers to two decimal places.
1.96(
B.σ)1.96(. n1)<≤ n≤ n≤ n≤n
​ to estimate the mean number of days of hunting per hunter within 2 days with probability 0.95 is 4 hunters.

Answer 1

The formula for determining the minimum sample size is N = (z * σ) / EBM, where N is the sample size, z is the critical value, σ is the population standard deviation, and EBM is the desired margin of error. For this particular question, with a bound on the error of the estimate of 2 and a desired confidence level of 0.95, the minimum sample size required to estimate the mean number of days of hunting per hunter within 2 days with a probability of 0.95 is 4 hunters.

Step-by-step explanation:

The formula for determining the minimum sample size, N, is given by:

N = (z * σ) / EBM

Where:
N is the sample size
z is the critical value corresponding to the desired confidence level (α/2)
σ is the population standard deviation
EBM is the desired margin of error

In this case, we have B = 2 as the bound on the error of the estimate. Given that the desired confidence level is 0.95, the critical value for α/2 = 0.025 is 1.96.

Substituting these values into the formula, we have:
N = (1.96 * σ) / 2

Since we are trying to estimate the mean number of days of hunting per hunter within 2 days with a probability of 0.95, and we are given σ = 4, we can further simplify the formula:
N = (1.96 * 4) / 2
N = 3.92

Finally, rounding the value of N to the closest integer gives us a minimum sample size of 4 hunters.