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somebody please help me! 4. A drug manufacturer states that the mean amount of N

ID: 3132541 • Letter: S

Question

somebody please help me!

4. A drug manufacturer states that the mean amount of Naproxen Sodium, the active ingredient in reducing pain, in a tablet 220mg. A pharmacist wonders if the mean amount of Naproen Sodium is different from 220mg? She randomly selects 17 tablets, measures the amount of Naproxen Sodium in each, and obtains the following information. Use significance 0.01.

Box plot= All points inside fences.

Normal probability plot= All points inside bounds.

xbar(sample average)= 221.24 mg

s = 2.42mg

4A. What is the appropriate test procedure?

z-test of the mean

t-test of the mean

z-test of the proportion

none of these

4B. what is the appropriate set of hypotheses (H0, H1)?

mu=220, mu does not equal 220

mu does not equal 220, mu= 220

mu= 220, mu is less than 220

mu=220, mu is greater than 220

4C. what is the correct magnitude of the critical value?

2.583

2.921

2.235

2.120

4D. what is the correct value of the test statistic?

-2.11

+2.11

+0.49

+8.43

4E. what is the correct p-value for this test statistic?

0.025

0.050

0.020

0.100

4F. what is the correct confidence interval?

220.0, 222.4

219.2, 223.2

220.2, 222.2

219.5, 222.9

4G. what is the correct conclusion of this hypothesis test?

do not reject the null

reject the null

sometimes reject the null

do not reject the alternative

4H. is the mean amount of Naproxen Sodium significantly different from 220 mg?

yes

no

sometimes

depends on the distribution

Explanation / Answer

A.

t-test of the mean [ANSWER]

As we do not know the population standard deviation.

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b.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   220  
Ha:    u   =/   220   [ANSWER, A]

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c.
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    16          
tcrit =    +/-   2.920781622   [ANSWER, B]

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d.  
              
Getting the test statistic, as              
              
X = sample mean =    221.24          
uo = hypothesized mean =    220          
n = sample size =    17          
s = standard deviation =    2.42          
              
Thus, t = (X - uo) * sqrt(n) / s =    2.112665692 [ANSWER, B]

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e.
          
              
Also, the p value is              
              
p =    0.050697963   [ANSWER, B]

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f.      

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    221.24          
t(alpha/2) = critical t for the confidence interval =    2.920781622          
s = sample standard deviation =    2.42          
n = sample size =    17          
df = n - 1 =    16          
Thus,              
Margin of Error E =    1.714312503          
Lower bound =    219.5256875          
Upper bound =    222.9543125          
              
Thus, the confidence interval is              
              
(   219.5256875   ,   222.9543125   ) [ANSWER, D]

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g.

              
As P > 0.01, we   DO NOT REJECT THE NULL HYPOTHESIS.   [ANSWER, A]

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h.

NO. [ANSWER]