If the sample mean and standard deviation for fill weights o

If the sample mean and standard deviation for fill weights of 81 boxes are 11.98 oz and 0.16 oz, respectively Find a 99% confidence interval for the mean fill of the boxes Compare the two confidence intervals and comment on this. Interpret the meaning of the confidence interval you found in part (s)

Solution

a)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
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 =    11.98          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    0.16          
n = sample size =    81          
              
Thus,              
Margin of Error E =    0.034843804          
Lower bound =    11.9451562          
Upper bound =    12.0148438          
              
Thus, the confidence interval is              
              
(   11.9451562   ,   12.0148438   ) [ANSWER]

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b)

Note that              
Margin of Error E = z(alpha/2) * s / sqrt(n)              
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 =    0.005          
X = sample mean =    11.98          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    0.16          
n = sample size =    81          
              
Thus,              
Margin of Error E =    0.045792521          
Lower bound =    11.93420748          
Upper bound =    12.02579252          
              
Thus, the confidence interval is              
              
(   11.93420748   ,   12.02579252   ) [ANSWER]

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c)

The 99% confidence interval is wider than the 95% confidence interval. This is because the critical z score increases as confidence level increases.

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d)

We are 95% confident that the true mean fill weight is between 11.9451562 and 12.0148438. [ANSWER]