Question

Consider the filling of cereal packages. Suppose that industry regulations state that if the mean package weight is not 16 ounces or more for a population of packages with label weight 16 ounces, then the company will be prosecuted. In this situation we, as the regulators, could prosecute only if we found strong evidence that the mean package weight was less than 16 ounces. Thus, our objective is to verify that the mean package weight, is not 16.0 ounces or more. Suppose that for this problem the population standard deviation is s = 0.4 and we obtain a random sample of 25, with an average of 18 ounces. Assume α = 0.05. Is the population mean package weight more than 16.0 ounces?

Answer #1

Consider the filling of cereal packages. Suppose that
industry regulations state that if the mean package weight is not
16 ounces or more for a population of packages with label weight 16
ounces, then the company will be prosecuted. In this situation we,
as the regulators, could prosecute only if we found strong evidence
that the mean package weight was less than 16 ounces. Thus, our
objective is to verify that the mean package weight, is not 16.0
ounces or...

A manufacturer of chocolate candies uses machines to package
candies as they move along a filling line. Although the
packages are labeled as 8 ounces, the company wants the packages to
contain a mean of 8.17 ounces so that the probability of producing
a package that contains less than 8 ounces is very
small. A sample of 50 packages is selected periodically
and weighed, and the packaging process is stopped if there is
evidence that the mean packaged amount is statistically different...

A manufacturer of chocolate candies uses machines to package
candies as they move along a filling line. Although the packages
are labeled as 8 ounces, the company wants the packages to contain
a mean of 8.15 ounces so that the probability of producing a
package that contains less than 8 ounces is very small. A sample of
30 packages is selected periodically and weighed, and the packaging
process is stopped if there is evidence that the mean packaged
amount is...

1. Lloyd’s Cereal Company packages cereal in 1-pound boxes (1
pound = 16 ounces). It is assumed that the amount of cereal per box
varies according to a normal distribution with a mean of 1 pound
and a standard deviation of 0.08 pound. One box is selected at
random from the production line every hour, and if the weight is
less than 14 ounces, the machine is adjusted to increase the amount
of cereal dispensed. The probability that the amount...

A manufacturer of chocolate candies uses machines to package
candies as they move along a filling line. Although the packages
are labeled as eight ounces, the company wants the packages to
contain a mean of 8.17 ounces so that virtually none of the
packages contain less than eight ounces. A sample of 50 packages is
selected periodically, and the packaging process is stopped if
there is evidence that the mean amount packaged is different from
8.17 ounces. Suppose that in...

A manufacturer of chocolate candies uses machines to package
candies as they move along a filling line. Although the packages
are labeled as 8 ounces, the company wants the packages to contain
a mean of 8.17 ounces so that virtually none of the packages
contain less than 8 ounces. A sample of 50 packages is selected
periodically, and the packaging process is stopped if there is
evidence that the mean amount packaged is different from 8.17
ounces. Suppose that in...

A machine that is programmed to package 3.30 pounds of cereal is
being tested for its accuracy. In a sample of 49 cereal boxes, the
sample mean filling weight is calculated as 3.39 pounds. The
population standard deviation is known to be 0.14 pound.
[You may find it useful to reference the z
table.]
a-1. Identify the relevant parameter of
interest for these quantitative data.
The parameter of interest is the proportion filling weight of
all cereal packages.
The parameter...

A machine that is programmed to package 5.69 pounds of cereal is
being tested for its accuracy. In a sample of 100 cereal boxes, the
sample mean filling weight is calculated as 5.69 pounds. The
population standard deviation is known to be 0.05 pound. Use Table
1.
a-1.
Identify the relevant parameter of interest for these
quantitative data.
The parameter of interest is the average filling weight of all
cereal packages.
The parameter of interest is the proportion filling...

A machine that is programmed to package 18.7 ounces of cereal in
each cereal box is being tested for its accuracy. In a sample of 43
cereal boxes, the mean is 18.79 ounces. Assume that the population
standard deviation is 0.24 ounces. Can you conclude at the 5%
significance level that the machine is not working properly? That
is, can you conclude that the machine is either underfilling or
overfilling the cereal boxes?
1. To test: Ho: (Click to
select) β μ p x¯ α (Click
to...

A manufacturer of chocolate candies uses machines to package
candies as they move along a filling line. Although the packages
are labeled as 8 ounces, the company wants the packages to contain
a mean of 8.17 ounces so that virtually none of the packages
contain less than 8 ounces. A sample of 50 packages is selected
periodically, and the packaging process is stopped if there is
evidence that the mean amount packaged is different from 8.17
ounces. Suppose that in...

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