School enrollment officials expected a change in the distribution of the number

3.   School enrollment officials expected a change in the distribution of the number of students across grades and were not sure whether it is what they should have expected. Test the following data for goodness of fit at the .05 level.

Grade         1      2      3      4      5      6
# of students       309      432      346      432      369      329









4.   Gender differences in dream content are well documented. Suppose a researcher studies aggression content in the dreams of men and women. Each participant reports his or her most recent dream. Then each dream is judged by a panel of experts to have low, medium, or high aggression content. The observed frequencies are shown in the following matrix:



GENDER                        AGGRESSION CONTENT


                        Low         Medium         High
Female                     18            4         2
Male                        4            17         15

 
a. Is there a relationship between gender and the aggression content of dreams?  Test at the 0.01 level of significance.