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.

To determine the shape of the comparison distribution, we need to consider the shape of the population distribution (general population). In this case, the researcher has mentioned that the distribution of the degree of affection for fathers in the general population is skewed to the right.

When a distribution is skewed to the right, it means that the majority of the data is concentrated towards the lower values, and there is a longer tail towards the higher values. The mean (60) being lower than the median (not provided) also supports this notion of a right-skewed distribution.

Now, since we are comparing the scores of a specific group (new fathers) against the general population, we can expect that the new fathers' scores will also reflect a similar distribution, albeit with some differences.

Therefore, the shape of the comparison distribution for the scores of new fathers is also likely to be skewed to the right.