Question

To properly treat patients, drugs prescribed by physicians must have a potency that is accurately defined. Consequently, not only must the distribution of potency values for shipments of a drug have a mean value as specified on the drug's container, but also the variation in potency must be small. Otherwise, pharmacists would be distributing drug prescriptions that could be harmfully potent or have a low potency and be ineffective. A drug manufacturer claims that its drug is marketed with a potency of 5 ± 0.1 milligram per cubic centimetre (mg/cc). A random sample of four containers gave potency readings equal to 4.94, 5.10, 5.03, and 4.90 mg/cc.

(a) Do the data present sufficient evidence to indicate that the
mean potency differs from 5 mg/cc? (Use *α* = 0.05. Round
your answers to three decimal places.)

1-2. Null and alternative hypotheses:

3. Test statistic: *t*
=

4. Rejection region: If the test is one-tailed, enter NONE for the
unused region.

t |
> | |

t |
< |

(b) Do the data present sufficient evidence to indicate that the
variation in potency differs from the error limits specified by the
manufacturer? (HINT: It is sometimes difficult to determine exactly
what is meant by limits on potency as specified by a manufacturer.
Since it implies that the potency values will fall into the
interval 5.0 ± 0.1 mg/cc with very high probability—the implication
is *always*—let us assume that the range 0.2; or (4.9 to
5.1), represents 6*σ*, as suggested by the Empirical Rule.
Note that letting the range equal 6*σ* rather than
4*σ* places a stringent interpretation on the manufacturer's
claim. We want the potency to fall into the interval

5.0 ± 0.1

with very high probability.) (Use *α* = 0.05. Round your
answers to three decimal places.)

1-2. Null and alternative hypotheses:

3. Test statistic: *χ*^{2}
=

4. Rejection region: If the test is one-tailed, enter NONE for the
unused region.

χ^{2} > |

χ^{2} < |

Answer #1

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To properly treat patients, drugs prescribed by physicians must
not only have a mean potency value as specified on the drug's
container, but also the variation in potency values must be small.
Otherwise, pharmacists would be distributing drug prescriptions
that could be harmfully potent or have a low potency and be
ineffective. A drug manufacturer claims that his drug has a potency
of 5 ± 0.1 milligram per cubic centimeter (mg/cc). A random sample
of four containers gave potency readings...

To properly treat patients, drugs prescribed by physicians must
not only have a mean potency value as specified on the drug's
container, but also the variation in potency values must be small.
Otherwise, pharmacists would be distributing drug prescriptions
that could be harmfully potent or have a low potency and be
ineffective. A drug manufacturer claims that his drug has a potency
of 5 ± 0.1 milligram per cubic centimeter (mg/cc). A random sample
of four containers gave potency readings...

To properly treat patients, drugs prescribed by physicians must
not only have a mean potency value as specified on the drug's
container, but also the variation in potency values must be small.
Otherwise, pharmacists would be distributing drug prescriptions
that could be harmfully potent or have a low potency and be
ineffective. A drug manufacturer claims that his drug has a potency
of 5 ± 0.1 milligram per cubic centimeter (mg/cc). A random sample
of four containers gave potency readings...

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