A random sample of 81 items is taken producing a sample mean

A random sample of 81 items is taken producing a sample mean of 47 and a sample standard deviation of 5.89. Construct a 90% confidence interval to estimate the population mean. Consider the following data drawn from a normal distribution population: 4, 8, 12, 11, 14, 6, 12, 8, 9, 5 Construct a 90% confidence interval for the population mean.

Solution

1.

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    47          
z(alpha/2) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    5.89          
n = sample size =    81          
              
Thus,              
Margin of Error E =    1.076465318          
Lower bound =    45.92353468          
Upper bound =    48.07646532          
              
Thus, the confidence interval is              
              
(   45.92353468   ,   48.07646532   ) [ANSWER]

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