The Crown Bottling Company has just installed a new bottling process that will f

Question

The Crown Bottling Company has just installed a new bottling process that will fill 21-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable: Underfilling leads to customer complaints and overfilling costs the company considerable money. In order to verify that the filler is set up correctly, the company wishes to see whether the mean bottle fill, mu, is close to the target fill of 21 ounces. To this end, a random sample of 36 filled bottles is selected from the output of a test filler run. If the sample results cast a substantial amount of doubt on the hypothesis that the mean bottle fill is the desired 21 ounces, then the filler's initial setup will be readjusted. (a) The bottling company wants to set up a hypothesis test so that the filler will be readjusted if the null hypothesis is rejected. Set up the null and alternative hypotheses for this hypothesis test.

Explanation / Answer

a) Null hypothesis(H0): A hypothesis of no difference is called null hypothesis. In this example, alternative hypothesis(Ha) is two sided because we reject null hypothesis for both overfilling and underfilling.

b) Type I error: Rejecting H0 (or accepting Ha) when H0 is true.

Type II error: Accepting H0 when it is false. (Accepting H0 when H1 is true).

• H0: = 21 versus Ha: 21

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