A manufacturer of cereal states that the average weight of cereal in a box is =

ID: 3321068 • Letter: A

Question

A manufacturer of cereal states that the average weight of cereal in a box is = 10.50 ounces, with a standard deviation of = 0.21 ounces.

Suppose we decide to check the manufacturer's claim by randomly sampling 100 boxes of cereal and finding the mean weight of the samples.

a) Would we question the claim if x-bar = 10.48 ounces? Show work that supports your claim by calculating P(x-bar<=10.48)

b) Would we question the claim if x-bar = 10.45 ounces? Show work that supports your answer by calculating P(x-bar<=10.45)

c) For what value of n would we question the manufacturer's claim if x-bar = 10.49 ounces? Recall z = -1.645 when we begin to question the claim.

a)
z = (10.48 - 10.50)/(21/sqrt(100)) = -0.0095

p-value = 0.4962

There are not significant evidence to conclude that weight is less than 10.50

b)
z = (10.45 - 10.50)/(21/sqrt(100)) = -0.0238

p-value = 0.4905

There are not significant evidence to conclude that weight is less than 10.50

c)
For z = -1.645, we need to find n

-1.645 = (10.48 - 10.50)/(21/sqrt(n))

21/sqrt(n) = (10.48 - 10.50)/(-1.645)

21/sqrt(n) = 0.012158055

sqrt(n) = 21/0.012158055

sqrt(n) = 1727.2499

n = 2983392.421

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