Question

A random sample of 100 daily stock returns was taken. The average return in the sample appeared to be 4.81%. The population standard deviation is not known, but the sample standard deviation is known to be 0.9%.

a.  Calculate a 95% confidence interval for the average stock return

b. How big the sample size be for the margin of error of 0.1% at the confidence level 95%?

c. A fund manager claims that the average stock return is higher than 4.81%. Test the fund manager’s claim with the 5% level of significance.

Answer 1

Q.a)

Q.b)

For big sample size we used z -statistics

Margin of error = critical value * standard deviation
Z- Critical value at 0.05/2 = 0.025 confidence intervals is 1.96
Standard deviation of sample is 0.9
Margin of error = 0.1

0.1 = 1.96* (0.9/✓n)
(1.96*0.9) /0.1 = ✓n
17.64 = ✓n
(17.64)^2 = n
311.1696 = n

Big sample size is 311

Q.c)

there is not enough evidence to claim that the average stock return is higher than 4.81% at the 5% significance level.