#### Dr. Jayanthi Sankaran

##### Well-Known Member

209.2 Over the last two years, a fund produced an average monthly return of +3.0% but with monthly volatility of 10.0%. That is, assume the random sample size (n) is 24, with mean of 3.0% and sigma of 10.0%. Further, the population's returns are normal. Are the returns statistically significant, in other words, can we decide the true mean return is greater than Zero with 95% confidence?

a) No, the t-statistic is 0.85

**b) No, the t-statistic is 1.47**

c) Yes, the t-statistic is 2.55

d) Yes, the t-statistic is 3.83

n = 24, sample mean = 3.0% sigma = 10%,

**is mu>0 with 95%confidence?**

**t**=

__Sample mean - population mean__=

__3% - 0__%

**= 1.4697**,

**t**

**23, 95%**

**= 1.71**, two-tailed =

**2.07**

sigma/SQRT(n) 10%/SQRT(24)

No, the t-statistic = 1.4697 (1.4697<1.71)

No, the t-statistic = 1.4697 (1.4697<1.71)

Even if we assumed normal one-sided, 95% critical Z is 1.645 (1.4697 <1.645)

In the above question, while we compute the t statistic why are we comparing it with 95% critical Z - I was under the impression that n>30 for such a comparison.

Thanks!

Jayanthi