Do you feel lucky? Children in a psychology study were asked to solve some puzzles and were then given feedback on their performance. Then they were asked to rate how luck played a role in determining their scores.11 This variable was recorded on a 1 to 10 scale with 1 corresponding to very lucky and 10 corresponding to very unlucky. Here are the scores for 60 children:
(a) Use graphical methods to display the distribution. Describe any unusual characteristics. Do these characteristics cause you concern about using the t-based methods of this section? Explain your answer.
(b) Give a 95% confidence interval for the mean luck score
(c) Based on the distribution in part (a), one could argue that there are two distinct groups of children. With that in mind, explain why inference about the mean luck score may not be very useful.
(d) The children in this study were volunteers whose parents agreed to have them participate in the study. To what extent do you think your results would apply to all similar children in this community?