Question
Asked Nov 12, 2019
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Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 12 boxes. It is reasonable to assume that the population is approximately normal.

13.03
14.98
13.12
13.13
13.11
13.03
13.16
14.98
13.06
13.05
13.12
13.13

The quality control manager is concerned that the mean weight is actually less than 14 ounces. Based on the confidence interval, is there a reason to be concerned? Explain.

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Expert Answer

Step 1

According to the provided information, boxes of cereal are labeled as containing 14 ounces. In order to check the concern that mean weight is actually less than 14 ounces the required hypothesis can be constructed as:

Null hypothesis, there is no reason to be concerned that is the mean weight is actually equal to 14 ounces, H0:µ=14

Alternate hypothesis, there is a reason to be concerned that the mean weight is actually less than 14 ounces, H1:µ<14.

The sample size (n) = 12

The sample mean of the provided data can be obtained as:

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Sum of all values mean ()= Total values 13.03 14.98 ...+13.13 12 160.9 12 13.41

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Step 2

The sample standard deviation can be obtained as: 

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Σ-Χ n-1 (13.03-13.41) (14.98 -13.41) + +(13.13-13.41) 12 1 =0.735

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Step 3

The sample size is small (less than 30) and population standard deviation is unknown so the ...

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- t = 13.41-14 0.735 v12 =-2.781

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Hypothesis Testing

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