Question

2. To study the effect of caffeine on cognitive ability, a cognitive ability test was administered to 8 students under two conditions on different days: Condition A) Without caffeine, and Condition B) after the students enjoyed a pumpkin spice latte. The students were randomized to determine if they did Condition A first or Condition B first (on separate days). The following are the results from the test:

Student	Condition A	Condition B
1	68	69
2	87	88
3	61	65
4	59	63
5	85	92
6	68	67
7	67	78
8	48	53

• (a) Estimate a 90% confidence interval for the change in test score between Condition A and condition B.
• (b) Determine if there is evidence that caffeine improved performance on the cognitive ability tests at a fixed Type I error rate of 0.05.
• (c) What is the level of significance of the test that you conducted in part (b).

Answer 1

Answer a)

The degrees of freedom = n - 1 = 8 - 1 = 7

The significance level α = 0.10

The critical t value corresponding to df = 7 and α = 0.10 is 1.895

The confidence interval for paired sample is given as: đ +  tc*sd/sqrt(n)

Lower Limit = -4 - (1.895*3.817)/sqrt(8) = -6.557

Upper Limit = -4 + (1.895*3.817)/sqrt(8) = -1.443

Thus, 90% Confidence Interval = (-6.557, -1.443)

Answer b)

Thus, at a fixed Type I error rate of 0.05, there is enough evidence to claim that caffeine improved performance on the cognitive ability tests

Answer c)

The probability of making a type I error is α, which is also know as the level of significance. So, the level of significance of the test that you conducted in part (b) is 0.05.