Question

4. Two machines are used for filling glass bottles
with a soft-drink beverage. The filling

processes have known standard deviations s1 = 0.010 L, and s2 =
0.015 L, respectively. A

random sample of n1 = 25 bottles from machine 1 and n2 = 20 bottles
from machine 2,

results in average net contents of ?̅

# = 2.04 L, and ?̅

$ = 2.07 L.

a. Test the hypothesis that both machines fill to the same net
contents, using a = 0.05.

What are your conclusions?

b. Find the P-value for this test.

c. Construct a 95% two-sided confidence interval on the mean fill
volume

Answer #1

A soft drink filling machine, when in perfect adjustment, fills
bottles with 12 ounces of soft drink. A random sample of 25 bottles
is selected, and the contents are measured. The sample yielded a
mean content of 11.88 ounces, with a sample standard deviation of
0.16 ounce.
Set up the hypotheses, and with a .05 level of significance,
test to see if the machine is in perfect adjustment. Show your
work.

A soft drink filling machine, when in perfect adjustment, fills
the bottles with 12 ounces of soft drink. A random sample of 49
bottles is selected, and the contents are measured. The sample
yielded a mean content of 11.88 ounces with a standard deviation of
0.35 ounces.
A) Specify the rejection region for = 0.01. Reject H0
if
B) What is the conclusion

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...

The fill amount in 1-liter soft drink bottles is normally
distributed, with a mean of 1.0 liter and a standard deviation of
0.05 liter. If bottles contain less than 95% of the listed net
content (0.95 liters, in this case), the manufacturer may be
subject to penalty by the state office of consumer affairs. Bottles
that have a net content above 1.08 liters may cause excess spillage
upon opening. In an effort to reduce the number of bottles that
contain...

Carla Vista Company bottles and distributes B-Lite, a diet soft
drink. The beverage is sold for 60 cents per 16-ounce bottle to
retailers, who charge customers 75 cents per bottle. For the year
2020, management estimates the following revenues and costs. Sales
$1,980,000 Selling expenses—variable $110,000 Direct materials
430,000 Selling expenses—fixed 62,000 Direct labor 400,000
Administrative expenses—variable 26,000 Manufacturing
overhead—variable 420,000 Administrative expenses—fixed 133,200
Manufacturing overhead—fixed 280,000 (a) Prepare a CVP income
statement for 2020 based on management’s estimates. CARLA...

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