Question

A statistician estimated that the standard deviation of her measurements is 2 cm. What should be the size of the sample in order to be 99% confident that the error of her estimates of mean does not exceed 0.43 cm? (z* = 2.58, for 99% confidence level)
1. 144
2. 121
3. 169
4. 196

Answer 1

Correct Answer - Option 1 : 144

Given

Standard deviation σ = 2 cm

z = 2.58 for 99% confident level

Formula

Standard error = σ/√n

Calculation

SE= σ/√n

⇒ 2.58 × σ/√n  ≤ 0.43 here z = 2.58

⇒ √n = (2.58 × 2)/0.43

⇒ √n = 12

⇒ n = 144

∴ The size of the sample in order to be 99% confident that the error of her estimates of mean does not exceed 0.43 cm is 144