posted by Anonymous .
A researcher interested in relationships developed a questionnaire that measures the degree of affection adult men feel for their fathers. She has found that for the general population the distribution is skewed to the right, the mean degree of affection is 60, and the standard deviation is 16. The researcher now is wondering if men who themselves have just become new fathers will score higher on the scale than men in general. She samples a group of 100 new fathers and finds that their mean is 64.5.
What is the shape of the comparison distribution?
With the above data, I would find it hard to tell. I assume a higher score means more affection. Is there an assumption that the new fathers have a more positive view toward fatherhood and therefore more affection toward their fathers? Can you assume that a few new fathers might have lower affection, because they now perceive their fathers as being "bad" fathers? (I don't know.)
Do you have the median value too? If the median is significantly higher than the mean, it would be negatively skewed (to the left). If it is significantly lower, the distribution would be positively skewed (drawn out to the right). If they are both very close, the distribution would be relatively normal.
The standard deviation does not indicate percentages/proportions accurately in a skewed distribution.
I hope this helps. Thanks for asking.