8.9 The duration of treating a disease by an existing medication has a mean of 1

Question

8.9 The duration of treating a disease by an existing medication has a mean of 14 days. A drug company claims that a new medication can
reduce the treatment time. To test this claim, the new medication is tried on 60 patients and their times to recovery are recorded.

If the mean recovery time is 13.5 days and the standard deviation is 3 days in this sample, answer the following questions.

a.) Formulate the hypotheses and determine the rejection region of the test with a level
of = 0.05

b.) What is your decision?

c.)Repeat the above test using the p-value.

d.)Using =3 find the type II error probability of the test for the alternative ' = 13.

Explanation / Answer

Set Up Hypothesis
Null, H0: U=14
Alternate, H1: U<14
Test Statistic
Population Mean(U)=14
Sample X(Mean)=13.5
Standard Deviation(S.D)=3
Number (n)=60
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =13.5-14/(3/Sqrt(60))
to =-1.291
| to | =1.291
Critical Value
The Value of |t | with n-1 = 59 d.f is 1.671
We got |to| =1.291 & | t | =1.671
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -1.291 ) = 0.10087
Hence Value of P0.05 < 0.10087,Here We Do not Reject Ho

[ANSWERS]
a. Reject Ho , When to < -1.671
b. Failed to Reject Ho
c. P0.05 < 0.10087, Do not Reject Ho

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