is the difference from 19 4 to 21 6 due to chance alone or do differences exist in the overall populations of all the paintings received in the art gallery we establish the problem by assuming the null hypothesis that the mean is the same between the two sample sets and conduct a t test to test if the hypothesis is plausible 
since the number of data records is different n1 10 and n2 20 and the variance is also different the t value and degrees of freedom are computed for the above data set using the formula mentioned in the unequal variance t test section the t value is 2 24787 since the minus sign can be ignored when comparing the two t values the computed value is 2 24787 the degrees of freedom value is 24 38 and is reduced to 24 owing to the formula definition requiring rounding down of the value to the least possible integer value one can specify a level of probability alpha level level of significance p as a criterion for acceptance in most cases a 5 value can be assumed using the degree of freedom value as 24 and a 5 level of significance a look at the t value distribution table gives a value of 2 064 comparing this value against the computed value of 2 247 indicates that the calculated t value is greater than the table value at a significance level of 5 therefore it is safe to reject the null hypothesis that there is no difference between means the population set has intrinsic differences and they are not by chance 