One of the conditions that allows us to use ANOVA safely is that of equal (population) standard deviations. Can we assume that this condition is met in this case?

here are options
(a) No, since the three sample standard deviations are not all equal.
(b) No, since the population standard deviations are not given, so we cannot check this condition.
(c) Yes, since 5.7 - 4.9 < 2.
(d) Yes, since 5.7 / 4.9 < 2.

I got answer as C, I need someone to help me confrim this because I was confused to between C and D. Please help

To determine whether the condition of equal population standard deviations is met, we need to compare the sample standard deviations.

In this case, you mentioned that the three sample standard deviations are not all equal. This implies that option (a) is incorrect because it states that the sample standard deviations are equal.

Option (b) is also incorrect since we are not given the population standard deviations. Without knowing the exact values of the population standard deviations, we cannot directly observe if they are equal.

Now, let's evaluate options (c) and (d):

Option (c) states that the condition is met because 5.7 - 4.9 < 2. However, this reasoning is incorrect. The difference between 5.7 and 4.9 being less than 2 has no direct relationship to the equality of population standard deviations.

Option (d) states that the condition is met because 5.7 divided by 4.9 is less than 2. However, similar to option (c), this reasoning is also incorrect. The ratio of 5.7 to 4.9 being less than 2 has no direct relationship to the equality of population standard deviations.

Therefore, neither option (c) nor option (d) is correct. The correct answer, in this case, is option (b): No, since the population standard deviations are not given, so we cannot check this condition.