### Example:

### Average Yearly Returns of a Portfolio

During a 15-year period, the mean annual return on a portfolio we are analyzing is 9.5 percent a year. We want to see whether this record is sufficient evidence to support the conclusion that portfolio's underlying mean return is equal to 10 percent, the return of the portfolio's benchmark with a known standard deviation of σ = 7

Determine whether the null hypothesis **(H _{0}: μ = 10)** is rejected in favor of alternative hypothesis

**(H**or not rejected at the 0.05 level of significance

_{a}: μ ≠ 10)
**Test concerning a single mean (Population Variance Known)**

Hypothetic Mean

**μ**

_{0}**H _{0} : μ = 0 VS H_{a} : μ ≠ 0 **

**H _{0} : μ ≤ 0 VS H_{a} : μ > 0 **

**H _{0} : μ ≥ 0 VS H_{a} : μ < 0 **

Sample Mean

Population Standard Deviation

**σ**

Sample Size

**n**

Level of Significance

**α**