A financial analyst wanted to estimate the mean annual return on mutual funds. A random sample of funds' returns shows an average rate of 12%. If the population standard deviation is assumed to be 4%, the 95% confidence interval estimate for the annual return on all mutual funds is

A. 0.037773 to 0.202227

B. 3.7773% to 20.2227%

C. 59.98786% to 61.01214%

D. 51.7773% to 68.2227%

E. 10.988% to 13.012%

A financial analyst wanted to estimate the mean annual return on mutual funds. A random sample of 60 funds' returns shows an average rate of 12%. If the population standard deviation is assumed to be 4%, the 95% confidence interval estimate for the annual return on all mutual funds is

A. 0.037773 to 0.202227

B. 3.7773% to 20.2227%

C. 59.98786% to 61.01214%

D. 51.7773% to 68.2227%

E. 10.988% to 13.012%

Answer: E. 10.988% to 13.012%

Step-by-step explanation:

Given;

Mean x = 12%

Standard deviation r = 4%

Number of samples tested n = 60

Confidence interval is 95%

Z' = t (0.025) = 1.96

Confidence interval = x + / - Z' (r/√n)

= 12% + / - 1.96 (4%/√60)

= 12% + / - 0.01214%

Confidence interval = (10.988% to 13.012%)