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 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? Run the appropriate test at =0.05.

A different investigator conducts a second study to investigate whether there is a difference in mean PEF in children with chronic bronchitis as compared to those without. Data on PEF are collected and summarized below. Based on the data, is there statistical evidence of a lower mean PEF in children with chronic bronchitis as compared to those without? Run the appropriate test at a= 0.05.

Group

Number of Children

Mean PEF

Std Dev PEF

Chronic Bronchitis

25

281

68

No Chronic Bronchitis

25

319

74

Solution

Answer to question# 1)

Mean value M = 306

The claim is that the mean is less than 306

Thus the hypothesis is:

Null hypothesis: Ho : M = 306

Alternate hypothesis: Ha: M < 306

.

Given:

sample size n = 40

Sample mean x bar = 279

Sample standard deviation s = 71

.

formula of test statistic is:

t= (x bar - M) / (s/sqrt(n))

.

on plugging the values we get

t = (279 -306) / (71 /sqrt(40))

t = -2.40511

.

df = n -1

df = 40 -1

df = 39

.

For P value we know that it is left tailed test , with df = 39 and t value = -2.40511

we use the excel formula =t.dist.rt(2.40511,39)

We get P value = 0.010506

.

Inference: Since the P value 0.010506 < alpha 0.05 , we reject the null

.

conclusion: Thus we conclude that there is significant evidence to state that the claim is correct. Mean is less than 306