Peak expiratory flow PEF is a measure of a patients ability

Peak expiratory flow (PEF) is a measure of a patient’s ability to expel air from the lungs. Patients with asthma or other respiratory conditions often have restricted PEF. The mean PEF for children free of asthma is 306. An investigator wants to test whether children with chronic bronchitis have restricted PEF. A sample of 40 children with chronic bronchitis are studied and their mean PEF is 279. Assume the population standard deviation is 71. Is there statistical evidence of a lower mean PEF in children with chronic bronchitis? Run the appropriate test at =0.05. Give null and alternative hypotheses, calculate the test statistic (show your work), and give the conclusion including a comparison to alpha or the critical value to receive full credit.

Solution

Set Up Hypothesis
Null,mean PEF for children free of asthma is same H0: U>306
Alternate,c H1: U<306
Test Statistic
Population Mean(U)=306
Sample X(Mean)=279
Standard Deviation(S.D)=71
Number (n)=40
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =279-306/(71/Sqrt(39))
to =-2.405
| to | =2.405
Critical Value
The Value of |t | with n-1 = 39 d.f is 1.685
We got |to| =2.405 & | t | =1.685
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -2.4051 ) = 0.01051
Hence Value of P0.05 > 0.01051,Here we Reject Ho

we conclude that mean PEF for children free of asthma