Cotinine (C_12H_12N_2O) is an alkaloid in tobacco and is a relatively long lasti

ID: 3175851 • Letter: C

Question

Cotinine (C_12H_12N_2O) is an alkaloid in tobacco and is a relatively long lasting (half-life 10 to 27 hours, cleared in 2.3 to 6.2 days) metabolite of nicotine (half-life 2 hours, cleared by 11 hours). Cotinine levels in blood serum are widely and conveniently used as a biomarker for exposure to tobacco products. the following data came from a 1986 study that measured cotinine levels (n mole/L) in the saliva of 7 subjects who were smokers. None were "heavy smokers" and all abstained from smoking for a week prior to the study. Subjects were then required to smoke a single cigarette. Saliva samples were taken at 12 and 24 hours after the cigarette was smoked and cotinine levels measured. E & l.1986. Some properties of saliva cotinine measurements in indicting Round mean and SD to 2 decimal places and CV to 3. Note that CV is coefficient of variation and is to be reported here, as a proportion (0-1) Use math in R or manual arithmetic to create the "Decrease" variable as "After 12 hours" minus "After 24 hours, " Confidence intervals of means. Calculate using normal theory. Round to 2 decimal places.

Explanation / Answer

Solution:

1. Descriptive statistics:

Mean

After 12 hours

43.53

0.5393

After 24 hours

17.00

0.6763

Decreases

(81 - 25)= 56

(43.53 - 14)= 29.53

(0.539- 0.676)= -0.137

Step by Step Calculation:

For 12 hours:

Input: 73, 58, 67, 128, 74, 18, 147

Mean(µ) = (73 + 58 + 67 + 128 + 74 + 18 + 147)/7

Mean = 565/7
round (µ) = 81

here variance(2)is 1895.23527649

Sd=sqrt( 1895.23527649)

= 43.5343

Coefficient of Variance = /µ= 43.5343 / 80.7142
Coefficient of Variance = 0.5393

For 24 hours:

Input: 24, 27, 49, 22, 0, 11, 43

Mean(µ) = (24 + 27 + 49 + 22 + 0 + 11 + 43)/7
Mean = 176/7
round(µ) = 25

here variance(2)is 289.14281764

Sd=sqrt( 289.14281764 )

= 17.0042

Coefficient of Variance = /µ = 17.0042 / 25.1428
Coefficient of Variance = 0.6763.

2. Formula for the 95% confidence interval using normal theory is:

Standard error of the mean = SEM = S/N = 16.453

t(, N-1) = 2.447

Lower bound= M - (t(, N-1)*SEM =81 - 40.2585 = 40.7415

Upper bound = M + (t(, N-1)*SEM = 81 +40.2585 = 121.2585

NOTE: here M is mean of 12 hour and below i will show result of 24 hours also

Standard error of the mean = SEM = S/N = 6.427

t(, N-1) = 2.447

Confidence interval = M +/- (t(, N-1)*SEM)

Lower bound: 9.27

Upper bound: 40.73