A cereal producer makes cereal boxes with a stated weight of 759 grams. From a large lot of these boxes, a random sample of 7 boxes yielded an average of 795.3 grams and standard deviation of 17.8 grams. Construct a 99% confidence interval for µ, the mean weight of boxes in this lots. Based on your confidence interval, what business suggestion will you make to the producer?
(i)
= 795.3
s = 17.8
n = 7
df = 7 - 1 = 6
= 0.01
From Table, critical values of t = 3.707
Confidence Interval:
So,
Answer is:
(770.357, 820.243)
(ii)
Since all values in the confidence interval (770.357, 820.243) are greater than 759, we will suggest the producer that the cereal boxes are overweight.
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