Neuroscience researchers did a study of thirty collegeage su

Neuroscience researchers did a study of thirty college-age subjects. 10 participants received one of the following beverages: water, water plus caffeine, or water plus caffeine plus sugar.Participants underwent two MRI scans and also took a performance test. On the performance test, the water group scored 29.00 with a standard error of 1.33. The caffeine group scored 30.70with a standard error of1.33. The caffeine plus sugar group scored 30.75with a standard error of1.49.So N=10 for each group.

Create a 90% confidence interval for the caffeine group, using a table value of 1.645. The confidence interval is (Blank 1, Blank 2). Use three decimal places for your answers.

Solution

Note that              
              
Lower Bound = X - z(alpha/2) * se              
Upper Bound = X + z(alpha/2) * se              
              
where              
              
alpha/2 = (1 - confidence level)/2 =    0.05          
              
Thus,              
X = sample mean =    30.7          
z(alpha/2) = critical z for the confidence interval =    1.645          
se = standard error =    1.33          
              
              
Thus,              
              
Lower bound =    28.51215          
Upper bound =    32.88785          
              
Thus, the confidence interval is              
              
(   28.512   ,   32.888   ) [ANSWER]