Question

A sample of 50 securities listed on the FTSE, corresponding to the 65% of the total value traded, shows an average monthly return of 0.9%, with a

standard deviation of 2.8%. What is the estimate average monthly return by all securities listed on the FTSE with a confidence level of 95%?

Answer 1

Suppose denote monthly return of total traded value .

Then if we assume that xi's follow normal distribution then .

based on the sample:

n = 50

Critical value is given by t distribution with df = 50 - 1 = 49 (Calculated in R)

then 95% confidence interval is given by:

So 95% confidence interval is given by

(0.1042489, 1.695751)