A bakery makes doughnuts that are packaged in boxes with labels stating that the

Question

A bakery makes doughnuts that are packaged in boxes with labels stating that there are 12
doughnuts weighing a total of 42 oz. If the variation among the doughnuts is too large, some
boxes will be underweight and some will be overweight. The quality-control supervisor has
found that a mean of 3.50 oz and standard deviation of less than 0.06 oz are good numbers to
strive for. Construct a 95% confidence interval for the standard deviation to determine
whether we have a good batch of doughnuts for the following dozen:
{ 3.43 3.37 3.58 3.50 3.68 3.61 3.42 3.52 3.66 3.50 3.36 3.42 }

Explanation / Answer

Sample mean = 3.504
Sample S.D. = 0.109
D.F. = 12-1 =11
Now 100(1-a)% C.I. for sigma is

sqrt((n-1)2s^2)/X2R) < < sqrt((n-1)2s2)/X2L

Where X2R & X2L are right & left limits of chi-square.

now for degree of freedom = 11

now X2R = 21.92(look at .025) & X2L = 3.82(look at .975)

So 95% C.I. for is .602 < < 3.405

We require standard deviation of less than 0.06 oz

so our C.I. does not match our criteria.

SO we are not producing good batch of doughnuts

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