Question

A quality-control engineer wants to find out whether or not a new machine that fills bottles with liquid has less variability than the machine currently in use. The engineer calibrates each machine to fill bottles with 16 ounces of a liquid. After running each machine for 5 hours, she randomly selects 15 filled bottles from each machine and measures their contents. Use the data below.

Old Machine

16.01

16

16.04

16.1

15.92

16.04

16.07

16.05

16.01

16.16

15.96

15.89

15.91

16

15.92

New Machine

16.02

15.95

16

16.06

16.08

15.96

15.99

15.97

16.05

15.96

16.05

16.02

16.03

15.94

15.95

State the Requirements to perform this test:

Perform a Hypothesis Test:

Answer #1

A quality-control engineer wants to find out whether or not a
new machine that fills bottles with liquid has less variability
than the machine currently in use. The engineer calibrates each
machine to fill bottles with 16 ounces of a liquid. After running
each machine for 5 hours, she randomly selects 15 filled bottles
from each machine and measures their contents. She obtains the
following results:
Old Machine
New Machine
16.01
16.02
16.04
15.96
15.96
16.05
16
15.95
16.07
15.99...

Two machines are used for filling plastic bottles (for a
desired volume of 16 ounces). The fill volume can be
assumed Normal, with standard deviations
σ1=0.020 and
σ2=0.025 ounces for the two machines
respectively. The quality control engineer wants to check if both
machines fill the bottles to the same volume or if the volumes
differ. A random sample of 10 bottles is taken from each
machine. Assume the data are independent. The data are given
below:
Machine_01
Machine_02
16.03...

Coca-cola is testing a new processing line for filling 16-oz.
bottles. They perform a test run in which 100 cases, each
containing 24 bottles, are completed. From this test-run they
randomly select 6 cases and take measurements on 5 randomly
selected bottles from each case. Results for each of the six cases
are shown in the table below. Estimate the average number of ounces
per bottle and provide an appropriate error bound for your
estimate.
Case
Average Fill for the...

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