Listed below are brain volumes cm3 of unrelated subjects use

Listed below are brain volumes (cm³) of unrelated subjects used in a study. Use the sample data to construct a 99% confidence interval estimate of the mean of the brain volume of the population.

963

1027

1272

1079

1070

1173

1067

1347

1100

1204

Please show calculation and formula used thank you :)

Solution

Getting the mean and standard deviation,

X (mean)= 1130.2
s = standard deviation = 117.4476716

As the sample size is small, n = 10 < 30, we use the t distirbution.

              
Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
              
X = sample mean =    1130.2          
t(alpha/2) = critical z for the confidence interval =    3.249835542          
s = sample standard deviation =    117.4476716          
n = sample size =    10          
              
Thus,              
              
Lower bound =    1009.50041          
Upper bound =    1250.89959          
              
Thus, the confidence interval is              
              
(1009.50041   ,   1250.89959)