The grade point averages GPA for 12 randomly selected colleg

The grade point averages (GPA) for 12 randomly selected college students are 2.1, 3.4, 2.6, 1.7,0.8, 4.0, 2.5, 1.1, 3.8, 0.5, 2.1,3.3. (a) find the sample mean (b) Find the sample standard deviation, (c) construct a 90% confidence interval for the population mean

Solution

A)

By technology, we have

X = sample mean =    2.325   [ANSWER]      

B)

By technology, we have

s = sample standard deviation =    1.161601559 [ANSWER]

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c)  

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    2.325          
t(alpha/2) = critical t for the confidence interval =    1.795884819          
s = sample standard deviation =    1.161601559          
n = sample size =    12          
df = n - 1 =    11          
Thus,              
              
Lower bound =    1.72279405          
Upper bound =    2.92720595          
              
Thus, the confidence interval is              
              
(   1.72279405   ,   2.92720595   ) [ANSWER]