Question

Suppose you are sampling the returns of exchange traded funds (ETF) which you assume to be normally distributed with unknown mean and known variance σ2 = 0.1 You want to find an interval of width 0.02 such that you are 95% confident the true mean lies within it. How many ETFs do you have to sample?

You may use −z0.975 = z0.025 = 1.96, where for Z ∼ N(0,1), Pr(Z ≥ zα) = α.

Answer 1

Solution :

Given that,

² = 0.1

standard deviation = = 0.3162

width = 0.02

margin of error = E = width / 2 = 0.02 / 2 = 0.01

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 0.3162) / 0.01)²

= 3841.6 = 3842

3842 ETFs you have to sample .