To properly treat patients, drugs prescribed by physicians must not only have a

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 4.95, 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 ? = 0.05.) State the null and alternative hypotheses. H0: ? = 5 versus Ha: ? < 5 H0: ? = 5 versus Ha: ? > 5 H0: ? < 5 versus Ha: ? > 5 H0: ? = 5 versus Ha: ? ? 5 H0: ? ? 5 versus Ha: ? = 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.

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

b) There is sufficient evidence to indicate that the mean potency differs from 5 mg/cc. H0 is rejected.

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

d)There is sufficient 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.

H0: ?2 = 0.0011 versus Ha: ?2 < 0.0011

H0: ?2 = 0.2 versus Ha: ?2 > 0.2

H0: ?2 = 0.0011 versus Ha: ?2 > 0.0011

H0: ?2 = 0.2 versus Ha: ?2 ? 0.2

H0: ?2 > 0.0011 versus Ha: ?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.

H0 is rejected. There is insufficient evidence to indicate that the variation in potency differs from the specified error limits.

H0 is rejected. There is sufficient evidence to indicate that the variation in potency differs from the specified error limits.

H0 is not rejected. There is insufficient evidence to indicate that the variation in potency differs from the specified error limits.

H0 is not rejected. There is sufficient evidence to indicate that the variation in potency differs from the specified error limits. You may need to use the appropriate appendix table or technology to answer this question.

Explanation / Answer

as per share qualities I am answering 1 part with multiple sub-parts:

ho: u=5 v/s h1: u =/= 5

Mean= 5.00 AVERAGE
sd= 0.09 STDEV
u= 5
n= 4.00 COUNT
alpha= 5%

Test statistic, t = (mean-u)/(sd/sqrt(n))
= (4.995-5)/(0.088128693776015/sqrt(4))
-0.114

Critical value, T(a/2,n-1)
t(0.05/2,4-1)
3.182

Rejection region,
t > 3.182
t <-3.182

P-value
2*(1-P(T<|t|)
2*(1-P(T<abs(-0.1135))
T.DIST.2T(abs(-0.1135),4-1)
0.9168

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

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