3 squirrels were found to have an average weight of 93 ounce

3 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight. Assume the weights of squirrels are normally distributed.

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Solution

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Here, we use the normal distrbution z, as the weights are normally distributed.

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 =    0.025          
X = sample mean =    9.3          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    1.1          
n = sample size =    3          
              
Thus,              
              
Lower bound =    8.055255693          
Upper bound =    10.54474431          
              
Thus, the confidence interval is              
              
(   8.055255693   ,   10.54474431   ) [ANSWER]