Use the given degree of confidence and sample data to constr

Use the given degree of confidence and sample data to construct a confidence interval for the population mean . Assume that the population has a normal distribution. n = 10, top enclose x = 12.8, s = 4.9, 95 percent 9.29 < < 16.31 9.31 < < 16.29 9.96 < < 15.64 9.35 < < 16.25

Solution

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
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 =    0.025          
X = sample mean =    12.8          
t(alpha/2) = critical t for the confidence interval =    2.262157163          
s = sample standard deviation =    4.9          
n = sample size =    10          
df = n - 1 =    9          
Thus,              
Margin of Error E =    3.505248839          
Lower bound =    9.294751161          
Upper bound =    16.30524884          
              
Thus, the confidence interval is              
              
(   9.29   ,   16.31   ) [ANSWER, OPTION A]