Question

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 equal to 4.94, 5.10, 5.02, and 4.90 mg/cc.

(a) Do the data present sufficient evidence to indicate that the
mean potency differs from 5 mg/cc? (Use ? = 0.05.)

State the null and alternative hypotheses.

*H*_{0}: ? ? 5 versus *H*_{a}: ? =
5*H*_{0}: ? = 5 versus *H*_{a}: ?
> 5 *H*_{0}: ? = 5 versus
*H*_{a}: ? ? 5*H*_{0}: ? < 5
versus *H*_{a}: ? > 5*H*_{0}: ? =
5 versus *H*_{a}: ? < 5

State the test statistic. (Round your answer to three decimal
places.)

*t* =

State the rejection region. (If the test is one-tailed, enter NONE
for the unused region. Round your answers to three decimal
places.)

t > |

t < |

State the conclusion.

*H*_{0} is not rejected. There is insufficient
evidence to indicate that the mean potency differs from 5
mg/cc.*H*_{0} is rejected. There is sufficient
evidence to indicate that the mean potency differs from 5
mg/cc. *H*_{0} is not
rejected. There is sufficient evidence to indicate that the mean
potency differs from 5 mg/cc.*H*_{0} is rejected.
There is insufficient evidence to indicate that the mean potency
differs from 5 mg/cc.

(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 he implies that the potency values will fall into the
interval 5 ± 0.1 mg/cc with very high probability—the implication
is almost *always*—let us assume that the range 0.2, or 4.9
to 5.1, represents 6?, as suggested by the Empirical Rule. Use ? =
0.05.)

State the null and alternative hypotheses.

*H*_{0}: ?^{2} = 0.0011 versus
*H*_{a}: ?^{2} <
0.0011*H*_{0}: ?^{2} = 0.2 versus
*H*_{a}: ?^{2} >
0.2 *H*_{0}: ?^{2}
> 0.0011 versus *H*_{a}: ?^{2} <
0.0011*H*_{0}: ?^{2} = 0.2 versus
*H*_{a}: ?^{2} ? 0.2*H*_{0}:
?^{2} = 0.0011 versus *H*_{a}: ?^{2}
> 0.0011

State the test statistic. (Round your answer to three decimal
places.)

?^{2} =

State the rejection region. (If the test is one-tailed, enter NONE
for the unused region. Round your answers to three decimal
places.)

?^{2} > |

?^{2} < |

State the conclusion.

*H*_{0} is rejected. There is sufficient evidence
to indicate that the variation in potency differs from the
specified error limits.*H*_{0} is not rejected.
There is insufficient evidence to indicate that the variation in
potency differs from the specified error
limits. *H*_{0} is not
rejected. There is sufficient evidence to indicate that the
variation in potency differs from the specified error
limits.*H*_{0} is rejected. There is insufficient
evidence to indicate that the variation in potency differs from the
specified error limits.

Answer #1

Q 1)

a) Null and Alternative Hypothesis :

H0: ? = 5 versus Ha: ? ? 5

The sample mean is

The sample standard deviation

Under H0, the test statistic is

Degrees of freedom = n-1= 3

Significance level

The critical value of t for 3 df at 5% significance level is 3.182

Decision Rule : Reject H0, if t > 3.182 or t< -3.182

Conclusion : Since calculated t fall with in the range of critical values. FAil to REject H0.

Hence, **H0 is not rejected. There is insufficient
evidence to indicate that the mean potency differs from 5
mg/cc.**

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...

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...

A manufacturer of hard safety hats for construction workers is
concerned about the mean and the variation of the forces helmets
transmit to wearers when subjected to a standard external force.
The manufacturer desires the mean force transmitted by helmets to
be 800 pounds (or less), well under the legal 1,000-pound limit,
and ? to be less than 40. A random sample of n =
45 helmets was tested, and the sample mean and variance were found
to be equal...

A manufacturer of hard safety hats for construction workers is
concerned about the mean and the variation of the forces helmets
transmit to wearers when subjected to a standard external force.
The manufacturer desires the mean force transmitted by helmets to
be 800 pounds (or less), well under the legal 1,000-pound limit,
and σ to be less than 40. A random sample of n = 45 helmets was
tested, and the sample mean and variance were found to be equal...

An experiment was conducted to test the effect of a new drug on
a viral infection. After the infection was induced in 100 mice, the
mice were randomly split into two groups of 50. The first group,
the control group, received no treatment for the
infection, and the second group received the drug. After a 30-day
period, the proportions of survivors, p?1 and
p?2, in the two groups were found to be 0.38 and 0.66,
respectively.
(a) Is there sufficient...

A random sample of 100 observations from a quantitative
population produced a sample mean of 21.5 and a sample standard
deviation of 8.2. Use the p-value approach to determine whether the
population mean is different from 23. Explain your conclusions.
(Use α = 0.05.) State the null and alternative hypotheses. H0: μ =
23 versus Ha: μ < 23 H0: μ = 23 versus Ha: μ > 23 H0: μ = 23
versus Ha: μ ≠ 23 H0: μ <...

Independent random samples of
n1 = 170
and
n2 = 170
observations were randomly selected from binomial populations 1
and 2, respectively. Sample 1 had 96 successes, and sample 2 had
103 successes.
You wish to perform a hypothesis test to determine if there is a
difference in the sample proportions
p1
and
p2.
(a)
State the null and alternative hypotheses.
H0:
(p1 − p2)
< 0 versus Ha:
(p1 − p2)
> 0
H0:
(p1 − p2)
= 0...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 21 minutes ago

asked 36 minutes ago

asked 50 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago