Peak expiratory flow (PEF) is a measure of a patient’s ability to expel air from

Question

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.

Explanation / Answer

null hypothesis: mean =306

and alternate hypothesis: mean<306

std error =std deviation/(n)1/2 =11.226

test stat =(X-mean)/std error =(279-306)/11.226=-2.405

for 0.05 level; rejection region z<-1.64485

as test stat z falls into rejection region we reject null hypothesis, and conclude that there is evidence of a lower mean PEF in children with chronic bronchitis

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