Question

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. Is Elizabeth's score significantly different from typical students her age?

1) State both the null and research hypothesis (just state them verbally, no greek symbols needed)

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.

Answer 1

(1) We have to test whether the Elizabeth's working memory is significantly different than other students her age

Null hypothesis: Elizabeth's working memory is same as other students her age

Alternate hypothesis: Elizabeth's working memory is significantly different than other students her age

(2) We have population mean () = 6, standard deviation () = 2 and sample mean 12

Using standard normal distribution table for z = 3.00, we get

p-value = 0.0027 < alpha level 0.05

Since the p value is less than alpha level, we will reject the null hypothesis.

Hence, we have sufficient evidence to conclude that Elizabeth's working memory is significantly different than other students her age.