# Hypothesis Testing with Cereal Package Weights

A cereal company claims that the weight of the cereal in one of the packages is at least 14 ounces. Eight packages are tested and the weights given below are measured. Test the claim at a=.0.01

14.6, 13.8, 14.1, 13.7, 14.0, 14.4, 13.6, 14.2

I have my null hypothesis as M (greater than or equal to) 14.0, and alternative hypothesis as M < 14.0

a=0.01

z = z > z.01 = .5000 - .0100 = .4900 ( Table A-2 indicates a value of 2.33)

x-m / s / sqroot of n = (14.05-14.0)/ (.105)/sqroot of 8 = 1.347

Am I doing this right? Do I have my null hypothesis correct? If not, please demonstrate.

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#### Solution Preview

Your Null Hypothesis is correct.

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<br>From The sample , Sample Mean = 14.05 ( you have it right)

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<br>Sample Std Deviation = ((Sum of (X-14.05)^2)/n-1)^.5

<br>Here n = 8 and ...