2. You are interested in comparing scores on the GRE-Psychology exam (GRE-P) of

Question

2. You are interested in comparing scores on the GRE-Psychology exam (GRE-P) of Psychology majors at a college with the population mean for all students who took the GRE-P last year nationwide. First assume that we don’t know the actual population mean for all students who took the exam nationwide but we want to create a 95% confidence interval for an estimate of the population mean. Now, assume that we have a sample of 97 Psychology students at a college who took the test and had a mean GRE-P score of 159.2. Also, assume that you know the standard error (x) = 1.50.

Find the 95% confidence interval for the population mean.

Explanation / Answer

Note that              
              
Lower Bound = X - z(alpha/2) * se              
Upper Bound = X + z(alpha/2) * se              
              
where              
              
alpha/2 = (1 - confidence level)/2 =    0.025          
              
Thus,              
X = sample mean =    159.2          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
se = standard error =    1.5          
              
              
Thus,              
              
Lower bound =    156.260054          
Upper bound =    162.139946          
              
Thus, the confidence interval is              
              
(   156.260054   ,   162.139946   ) [ANSWER]

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