I need some help with statistics ?

Since you are testing a population variance (standard deviation squared), you must use the Chi-Square distribution(which is based on the Z dist., hence the normality umption). Since the statistician believes the SD to be less than 25, a lower tail test is appropriate. A lower tail critical Chi-Square is based on two arguments: degrees of freedom, which is sample size -1 (20-1=19), and 1-alpha (1-.05=.95). Based on the above, the critical Chi-Square found in any stat book or software should be 10.117.