Refer to the Advances in Cognitive Psychology (Jan. 2013) study of influencing performance in a classic psychological test that involved adding a set of numbers, Exercise 9.66 (p. 471). Recall that one group of students saw each of the numbers for 2 seconds on the screen while a second group saw all the numbers on the screen at the same time, with the number 1,000 presented in bright red. The researchers want to estimate the true difference in the proportions of students in the two groups that give the correct answer with a 95% confidence interval. They want to know how many students to sample in each group in order to obtain an estimate that is no more than .10 from the true difference.
a. Identify the parameter of interest for this study.
b. What is the desired confidence level?
c. What is the desired sampling error?
d. Find the sample size required to obtain the desired estimate. Assume n1 = n2.
e. Repeat part d, but now assume that twice as many students will be sampled in the first group as in the second group, i.e., assume n1 = 2n2.