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 is 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? (α = 0.05, enter 1 for “yes”, and 0 for “no”).

Answer 1

Answer : 1    (YES)

Explanation

Data Summary
	Mean (M)	Sample Size (n)	Standard Deviation (SD)
Population	306
Sample	279	40	71

The null and alternative hypotheses are                      
Ho : μ = 306       μ is the population mean for PEF     
Ha : μ < 306                      
                      
α = 0.05                      
We use T test since population standard deviation is unknown, and sample size is small                      
Using the below formula, we get the test statistic                      
           
Degrees of Freedom                      
df = n - 1 = 39                      
                      
t-statistic                      
t-statistic = -2.4051                      
                      
For t = -2.4051 df = 39 we find the Left Tailed p-value using Excel function t.dist                      
                      
p-value = t.dist(-2.4051, 39, TRUE)                      
p-value = 0.0105                      
                      
Decision                      
0.0105 < 0.05                      
that is p-value <= α                      
Hence we REJECT Ho                      
                      
Conclusion                      
There exists enough statistical evidence at α = 0.05 to show that the children with chronic bronchitis have restricted PEF