Our decisions depend on how the options are presented to us. Here's an experiment that illustrates this phenomenon. Tell 20 subjects that they have been given $50 but can't keep it all. Then present them with a long series of choices between bets they can make with the $50. Scattered among these choices in random order are 64 choices between a fixed amount and an all-or-nothing gamble. The odds for the gamble are always the same, but 32 of the fixed options read "Keep $20" and the other 32 read "Lose $30". These two options are exactly the same except for their wording, but people are more likely to gamble if the fixed option says they lose money. Here are the percent differences ("Lose $30" minus "Keep $20") in the numbers of trials on which the 20 subjects chose to gamble:
37.5 30.8 6.2 17.6 14.3 8.3 16.7 20.0 10.5 21.7
30.8 27.3 22.7 38.5 8.3 10.5 8.3 10.5 25.0 7.7
(a) Make a stemplot. Is there any sign of a major deviation from Normality?
(b) All 20 subjects gambled more often when faced with a sure loss than when faced with a sure win. Give a 95% confidence interval for the mean percent increase in gambling when faced with a sure loss.
Step-by-step calculation of 95% confidence interval for the mean percent increase in gambling. A stemplot of the variable with comments on its normality is included.