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...

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 with a standard deviation of 71.

Is there statistical evidence of a lower mean PEF in children with chronic bronchitis?  Run the appropriate test at a=0.05.

Please
perform the hypothesis test manually, and state the chosen test statitic's by name.