Grinding balls after a certain length of time in mill slurry

Grinding balls after a certain length of time in mill slurry is 3.42 with a standard deviation of 0.68 gram. The 99% confidence interval for the true mean weight loss of such grinding balls under the stated conditions is A claim is made that the me an weight loss is equal to 3.35 grams at the 0.01 level of significance. Is this claim true? Use the confidence interval approach to evaluate this claim. Enter 0 for FALSE or 1 for TRUE:

Solution

Note that              
              
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 =    0.005          
X = sample mean =    3.42          
t(alpha/2) = critical t for the confidence interval =    2.946712883          
s = sample standard deviation =    0.68          
n = sample size =    16          
df = n - 1 =    15          
Thus,              
              
Lower bound =    2.91905881          
Upper bound =    3.92094119          
              
Thus, the confidence interval is              
              
2.91905881<u<3.92094119   [ANSWER]

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As we can see, 3.35g is within the interval above.

HENCE, THE CLAIM IS TRUE. [ANSWER, 1]