Question

A cereal manufacturer is concerned that the boxes of cereal not be under filled or overfilled.

Each box of cereal is supposed to contain 13 ounces of cereal.

A random sample of 31 boxes is tested.

The average weight is 12.58 ounces and the standard deviation is 0.25 ounces.


Calculate a confidence interval to test the hypothesis at a=.10

Answer 1

Explanation:

given that

A cereal manufacturer is concerned that the boxes of cereal not be under filled or overfilled.

Each box of cereal is supposed to contain 13 ounces of cereal.

A random sample of 31 boxes is tested.

The average weight is 12.58 ounces and the standard deviation is 0.25 ounces.

Sample mean = 12.58

Sample std deviation = 0.25

Sample size = 31

Sample std error =
`\sqrt{(0.25)/(√(31) ) } \\=0.0449`

confidence interval can be calculated using t critical value because population sd is not known.

df = 30

t critical for two tailed = 1.697

Margin of error =
`1.697*0.0449\\=0.07620`

conidence interval =
`(12.58-0.0762, 12.58+0.0762)\\=(12.5038, 12.6562)`

Since this does not contain 13 oz. we reject the claim that each box contains exactly 13 oz.