Homework SourseAn investigator conducts a study to investigate whether ther
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?
Apply the two sample t test at alpha=0.05.
Z 95% Confidence Interval
Upper Limit 95% CI
Lower Limit 95% CI
Based on the data, is there statistical evidence of a lower mean PEF in children with chronic bronchitis as compared to those without?
Apply the two sample t test at alpha=0.05.
Z 95% Confidence Interval
Upper Limit 95% CI
Lower Limit 95% CI
Based on comparing the critical the upper and lower limits of the confidence interval for the mean PEF for children with No Chronic Bronchitis to the mean PEF for children With Bronchitis which of the following is (are) true.
a. There is statistical evidence of a lower mean PEF in children with chronic bronchitis as compared to those without
b. There is not statistical evidence of a lower mean PEF in children with chronic bronchitis as compared to those without
c. The confidence interval contains the mean PEF for the No Chronic Bronchitis group
d. A and C
GROUP NUMBER OF CHILDREN Mean PEF Std Dev PEF
Chronic Bronchitis 25 281 68
No Chronic Bronchitis 25 319 74
Solution
The degree of freedom =n1+n2-2=25+25-2=48
Given a=0.05, t(0.025, df=48) =2.01 (from student t table)
Upper Limit 95% CI:
(xbar1-xbar2) + t*sqrt(s1^2/n1+s2^2/n2)
=(281-319)+2.01*sqrt(68^2/25+74^2/25)
=2.4005
Lower Limit 95% CI:
(xbar1-xbar2) - t*sqrt(s1^2/n1+s2^2/n2)
=(281-319)-2.01*sqrt(68^2/25+74^2/25)
=-78.4005
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b. There is not statistical evidence of a lower mean PEF in children with chronic bronchitis as compared to those without
