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
In what case?
To determine whether the condition of equal population standard deviations is met, we can compare the sample standard deviations. The correct option in this case is (a) "No, since the three sample standard deviations are not all equal."
Option (b) states that we cannot check this condition since the population standard deviations are not given. However, even with sample standard deviations, we can compare them to determine if they are equal.
Option (c) compares the difference between the two sample standard deviations, which is not the correct approach for evaluating equality of standard deviations. Comparing the absolute difference between two standard deviations does not provide information about whether they are statistically equal.
Option (d) compares the ratio of the two standard deviations and states that if this ratio is less than 2, then the condition is met. However, there is no established rule that suggests a ratio less than 2 indicates equality of standard deviations.
Therefore, the correct option is (a) "No, since the three sample standard deviations are not all equal."