Question

# To properly treat patients, drugs prescribed by physicians must have a potency that is accurately defined....

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 6σ, as suggested by the Empirical Rule. Note that letting the range equal 6σ rather than 4σ 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:    χ2 =

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

 χ2 > χ2 <

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