### Example

We are analyzing Sendar Equity Fund, a midcap growth fund that has been in existence for 24 months. During this period, it has achieved a mean monthly return of 1.50 percent with a sample standard deviation of monthly returns of 3.60 percent.

We want to test a claim that the particular investment disciplines followed by Sendar result in a standard deviation of monthly returns of less than 4 percent (being careful to square standard deviation to obtain a test in terms of variance).

Determine whether the null hypothesis \[ (\ H_0: σ^2 ≥ 16.0 \ ) \ \]

is rejected in favor of alternative hypothesis \[ ( \ H_a: σ^2 < 16.0 \ ) \ \]

or not rejected at the 0.05 level of significance.

**Tests Concerning a Single Variance**

Sample Standard Deviation ( \[ S \] )

Sample Size ( \[ n \] )

Level of Significance ( \[ α \] )

Hypothetic Value ( \[ σ_0^2 \] )