Question

The Crown Bottling Company has just installed a new bottling process that will fill 20-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, µ, is close to the target fill of 20 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 20 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.

*H _{0}*:

**(b)** In the context of this situation, interpret
making a Type I error; interpret making a Type II error.

Type I error: decide
µ |
(Click to select)?=?? | 20 when µ |
(Click to select)???= | 20. |

Type II error: decide
µ |
(Click to select)?=?? | 20 when µ |
(Click to select)=??? | 20. |

Answer #1

(a)

Since both overfilling and underfilling bottles are undesirable so alternative hypothesis will be two tailed. That is

The null hypothesis is

(b)

Type I: It is probability of rejecting the true null hypothesis.

That is you incorrectly conclude that filler need to be readjusted while actually it is not required.

Type II: It is probability of fail to reject the false null hypothesis.

That is you incorrectly conclude that filler do not need to be readjusted while actually it is required.

The Crown Bottling Company has just installed a new bottling
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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, μ, is close to the
target fill of 16 ounces. To this end, a random sample...

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