Ben, Hugh, and Alex wanted to determine if the size of the football made a difference in

Question:

Ben, Hugh, and Alex wanted to determine if the size of the €œfootball€ made a difference in scoring accuracy in the game of paper football. (Details of the simple tabletop game can be found at www. paperfootball. us.) In addition, these students were interested in knowing if the effect of football size was dependent on a player€™s experience level.
The researchers set up a goal that was 8 inches above a table and 10 inches wide. The subjects kicked/ flicked the football from 42 inches away from the goal.

Photo courtesy of Shonda Kuiper.
There were 18 volunteers, who self- identified as experienced or inexperienced players. After a few practice kicks, each subject kicked 20 small and 20 large footballs in random order (flipping a coin before each kick) at the goal. The response for this study was the proportion of successful goals.
a. Specify whether each factor in the study is fixed or random and whether each factor is crossed or nested with all other factors.
b. Calculate an appropriate ANOVA for this study using Proportion as the response. State your conclusions, taking into account random sampling and random allocation. Provide appropriate plots.
c. Check the model assumptions. Create a plot to check if the data appear to be skewed or have outliers. Is there reason to doubt the equal variance assumption? Are the error terms approximately normally distributed?
d. Draw a Hasse diagram corresponding to this study.