What is minimum sample needed if you know the SD is 22.36 and an accuracy of 3.06 and you want a confidence level of 90%

To determine the minimum sample size needed, we can use the formula:

n = (Z * σ / E)^2

Where:
n = minimum sample size
Z = Z-score corresponding to the desired confidence level
σ = standard deviation
E = desired accuracy or margin of error

In this case, we want a confidence level of 90%, which corresponds to a Z-score of approximately 1.645 (look up in the Z-table). The standard deviation (σ) is given as 22.36, and the desired accuracy (E) is 3.06.

Plugging in these values into the formula:

n = (1.645 * 22.36 / 3.06)^2

n = (36.7392 / 3.06)^2

n = 11.9995^2

n ≈ 144

Therefore, the minimum sample size needed is approximately 144.