Assignment task: Elizabeth is an 8-year-old student with an exceptional working memory ability. Her mother is very proud and seeks to determine if Elizabeth's working memory is significantly higher than other students her age so she is taken to a cognitive psychologist. Elizabeth is given the reverse digit span test where one is shown a sequence of numbers one at a time (i.e. 3, 6, 4, 7) and they must recite that list backwards (i.e. 7, 4, 6, 3). Elizabeth reachest a highest score of 12 numbers before making 3 errors in a row. The population average for all 8-year-olds is 6 numbers with a standard deviation of 2.
1) Is Elizabeth's score significantly different from typical students her age?
2) Provide Elizabeth's z score and determine if the score is significantly different from average at the .05 level using a 2-tailed test.