Final answer:
To determine if you should reject the null hypothesis with an F statistic of 2.55, compare it against the critical value for an F distribution with (6, 35) degrees of freedom at α = 0.05. If 2.55 is larger than the critical value, reject the null hypothesis; otherwise, do not reject.
Step-by-step explanation:
To answer whether you should reject the null hypothesis at α = 0.05, with a given F statistic of 2.55 from an experiment with k = 7 groups and total sample size n = 42, you need to compare the F statistic to the critical value from the F distribution table specific for your degrees of freedom and significance level. The degrees of freedom for the numerator (α) is k - 1, which is 7 - 1 = 6, and for the denominator (β), it's n - k, which is 42 - 7 = 35. Since this is a specific table lookup and the exact critical value isn't provided in the information, under regular circumstances you'd check an F distribution table or use software to find the critical value. If the F statistic is greater than the critical value, you reject the null hypothesis; otherwise, you fail to reject it.
The general rule, shown in various provided examples, is that if the calculated test statistic is larger than the critical value or if the p-value is less than the significance level (α), you reject the null hypothesis. Therefore, provided you have the correct critical value for an F distribution with (6, 35) degrees of freedom at α = 0.05, and if 2.55 exceeds that critical value, you would reject the null hypothesis. If not, you do not reject it.