Question

The Crown Bottling Company has just installed a new bottling
process that will fill 16-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 16 ounces. To this end, a random sample of 33 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 16 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.

**(b)** Suppose that Crown Bottling Company decides
to use a level of significance of *α* = 0.01, and suppose a
random sample of 33 bottle fills is obtained from a test run of the
filler. For each of the following four sample means— x¯x¯ = 16.05,
x¯x¯ = 15.95, x¯x¯ = 16.06, and x¯x¯ = 15.99 — determine whether
the filler’s initial setup should be readjusted. In each case, use
a critical value, a *p*-value, and a confidence interval.
Assume that σ equals .1. **(Round your z to 2 decimal places
and p-value to 4 decimal places and CI to 3 decimal
places.)**

x¯x¯ = 16.05

x¯x¯ = 15.95

x¯x¯ = 16.06

x¯x¯ = 15.99

Answer #1

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The Crown Bottling Company has just installed a new bottling
process that will fill 16-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 16 ounces. To this end, a random sample...

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Classic Cola soft drink. Both overfilling and underfilling bottles
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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
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