A hospital conducts stress tests to study the heart after someone has a heart at

Question

A hospital conducts stress tests to study the heart after someone has a heart attack. They are trying to reduce the turn-around times. Initially, the turn-around time for a test was 68 hours. After improving the process, they collected a sample of 50 turn-around times. In this sample, the mean turn-around-time was 32 hours, with a standard deviation of 9 hours.

a. If you test the null hypothesis, at the 0.01 level of significance, is there evidence that the new process has reduced turn-around times?

b. Interpret the meaning of the p-value of this problem.

Explanation / Answer

Set Up Hypothesis
Null Hypothesis H0: U=68
Alternate, New process has reduced turn-around times H1: U<68
Test Statistic
Population Mean(U)=68
Sample X(Mean)=32
Standard Deviation(S.D)=9
Number (n)=50
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =32-68/(9/Sqrt(49))
to =-28.284
| to | =28.284
Critical Value
The Value of |t | with n-1 = 49 d.f is 2.405
We got |to| =28.284 & | t | =2.405
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -28.2843 ) = 0
Hence Value of P0.01 > 0,Here we Reject Ho

Evidence to prove New process has reduced turn-around times

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