A 95 percent confidence interval for the mean of a population is to be constructedand must be accurate within 0.3 unit. A preliminary sample standard deviation is2.9. The smallest sample size n that provides the desired accuracy with 95 percentconfidence is:.A. 400 B. 359 C. 389 D. 253

B. 359

Step-by-step explanation:

Given that:

The margin of error (e) must be within 0.3 unit, The standard deviation (σ) = 2.9 and the the confidence level = 95% = 0.95

α = 1 =0.95 = 0.05

The z score of 0.025 corresponds to the z score of 0.0475 (0.5 - 0.025) which can be gotten from the normal probability table.

Therefore:

The formula for the margin of error is given by:

Therefore the smallest sample size (n) is 359

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.