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 to receive full credit. You MUST show your work to receive full credit.

Explanation / Answer

Given that,
population mean(u)=306
standard deviation, =40
sample mean, x =279
number (n)=71
null, Ho: =306
alternate, H1: <306
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 279-306/(40/sqrt(71)
zo = -5.68765
| zo | = 5.68765
critical value
the value of |z | at los 5% is 1.645
we got |zo| =5.68765 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : left tail - ha : ( p < -5.68765 ) = 0
hence value of p0.05 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: =306
alternate, statistical evidence of a lower mean PEF in children with chronic bronchitis H1: <306
test statistic: -5.68765
critical value: -1.645
decision: reject Ho
p-value: 0

we have statistical evidence of a lower mean PEF in children with chronic bronchitis

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