The winning teams score in 7 high school basketball games wa

The winning team\'s score in 7 high school basketball games was recorded. If the sample mean is 68.3 points and the sample standard deviation is 13.0 points, find the 98% confidence interval of the true mean. Assume the number of points follows a normal distribution.

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Solution

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Note that              
              
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 =    0.01          
X = sample mean =    68.3          
z(alpha/2) = critical z for the confidence interval =    2.326347874          
s = sample standard deviation =    13          
n = sample size =    7          
              
Thus,              
              
Lower bound =    56.86940097          
Upper bound =    79.73059903          
              
Thus, the confidence interval is              
              
(   56.86940097   ,   79.73059903   ) [ANSWER]