Question

Q2. 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. An investigator conducts a 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 α=0.05.  

Group	Number of Children	Mean PEF	Std Dev PEF
Chronic Bronchitis	42	265	65
No Chronic Bronchitis	40	319	70

a) Hypotheses (2 points)

                  HO:                                      vs.                                HA  

b) Calculate (2 points)

S²p=

c) Compute Test statistic (5 points)

T=

d) P-value (1 points)

e) Conclusion (1 point)(circle one )

             Accept H0                                              Reject H0

f) Calculate a 95% confidence interval for mean difference  (4 points)

Answer 1

a)

Ho:μ1-μ2	=	0
Ha: μ1-μ2	<	0

b)

Pooled Variance Sp2=((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=

4554.0625

c)

test stat t =(x1-x2-Δo)/Se=

-3.622

d)

p value : =

0.0003

e)

since p value <0.05

Reject H0

f)

for 95 % CI & 80 df value of t=			1.990
margin of error E=t*std error =			29.669133
lower bound=mean difference-E=			-83.669
Upper bound=mean differnce +E=			-24.331
from above 95% confidence interval for population mean =(-83.669,-24.331)