Measurements were made of the carbon monoxide (CO) transfer factor levels in sev
ID: 3218945 • Letter: M
Question
Measurements were made of the carbon monoxide (CO) transfer factor levels in seven smokers with chickenpox who were admitted to a hospital, and which were recorded with a view to determining their risk of contracting pneumonia. The measurements were taken when the patients entered the hospital and were repeated one week later. (a) Screen the data with a view to carrying out an appropriate parametric inference. (b) Investigate the hypothesis that there is no difference between the mean CO transfer factor levels in smokers at entry and after one week using a parametric test. (c) Determine a 90% confidence interval for this difference.Explanation / Answer
(a) I have screen the data with appropriate parametric inference.
(b) null HYpothesis : H0 : on entry = after one weekCO level after one week : Mean X2 = 68.14 ; std.dev s2 = 11.68CO level on Entry : Mean of sample X1 = 56 ; Std. dev. s1 = 8.64
Alternative Hypothesis : Ha : on entry after one week
so it would be two tailed paired t- test for mean dfference
Here Sample Mean of difference = after one week - on entry = 68.14 - 56 = 12.14
paired = 15.38 [ can check from above given table]
so for confidence interval is of 90% and degree of freedom dF = 7-1 = 6 here
=> (after one week - on entry ) +- t/2,6 [paired /sqrt(n)] = 12.14 +- 1.943 * (15.38 * sqrt(7) )
= (0.8452, 23.4348)
There is no zero in confidenceinterval so we can reject the null hypothesis and can say that there is significant difference in CO evel after one week.
Patient On Entry After one week Diference 1 40 73 33 2 50 52 2 3 56 80 24 4 58 85 27 5 60 64 4 6 62 63 1 7 66 60 -6 Mean 56 68.14285714 12.1428571 Variance 74.66667 136.4761905 236.47619 Std. dev. 8.640988 11.68230245 15.3777824