Question

Question 4. (20 pts.) The objectives of a study by Skjelbo et al. were to examine (a) the relationship between Chloroguanide metabolism and efficacy in malaria prophylaxis and (b) the mephenytoin metabolism and its relationship to chloroguanide metabolism among Tanzanians. From information provided by urine specimens from the 216 subjects, the investigators computed the ratio of unchanged S-mephenytoin to R-mephenytoin (S/R ratio). The results were as follows: 0.0269 0.0400 0.0550 0.0550 0.0650 0.0670 0.0700 0.0720 0.0760 0.0850 0.0870 0.0870 0.0880 0.0900 0.0900 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.1000 0.1020 0.1040 0.1050 0.1050 0.1080 0.1080 0.1090 0.1090 0.1090 0.1160 0.1190 0.1200 0.1230 0.1240 0.1340 0.1340 0.1370 0.1390 0.1460 0.1480 0.1490 0.1490 0.1500 0.1500 0.1500 0.1540 0.1550 0.1570 0.1600 0.1650 0.1650 0.1670 0.1670 0.1677 0.1690 0.1710 0.1720 0.1740 0.1780 0.1780 0.1790 0.1790 0.1810 0.1880 0.1890 0.1890 0.1920 0.1950 0.1970 0.2010 0.2070 0.2100 0.2100 0.2140 0.2150 0.2160 0.2260 0.2290 0.2390 0.2400 0.2420 0.2430 0.2450 0.2450 0.2460 0.2460 0.2470 0.2540 0.2570 0.2600 0.2620 0.2650 0.2650 0.2680 0.2710 0.2800 0.2800 0.2870 0.2880 0.2940 0.2970 0.2980 0.2990 0.3000 0.3070 0.3100 0.3110 0.3140 0.3190 0.3210 0.3400 0.3440 0.3480 0.3490 0.3520 0.3530 0.3570 0.3630 0.3630 0.3660 0.3830 0.3900 0.3960 0.3990 0.4080 0.4080 0.4090 0.4090 0.4100 0.4160 0.4210 0.4260 0.4290 0.4290 0.4300 0.4360 0.4370 0.4390 0.4410 0.4410 0.4430 0.4540 0.4680 0.4810 0.4870 0.4910 0.4980 0.5030 0.5060 0.5220 0.5340 0.5340 0.5460 0.5480 0.5480 0.5490 0.5550 0.5920 0.5930 0.6010 0.6240 0.6280 0.6380 0.6600 0.6720 0.6820 Mth 251 Page 2 (a) From these data construct the following distributions: frequency, relative frequency, cumulative frequency, and cumulative relative frequency; and the following graphs: histogram, frequency polygon. (b) The investigators defined as poor metabolizers of mephenytoin any subject with an S/R mephenytoin ratio greater than .9. How many and what percentage of the subjects were poor metabolizers? (c) How many and what percentage of the subjects had ratios less than .7? Between .3 and .6999 inclusive?

Answer 1

ANSWER:

Consider the class interval be 0.09

a)

Class interval	Frequency	Cumulative frequency	Relative	Cumulative relative
0-0.0899	13	13	0.068	0.068
0.09-0.1799	75	88	0.391	0.458
0.18-0.2699	32	120	0.167	0.625
0.27-0.3599	23	143	0.120	0.745
0.36-0.4499	24	167	0.125	0.870
0.45-0.5399	11	178	0.057	0.927
0.54-0.6299	10	188	0.052	0.979
0.63-0.7199	4	192	0.021	1.000

Histogram 80 70 60 50 40 30 20 Frequency hu 10 0 0.18-0.2699 0.63-0.7199 0-0.0899 0.09-0.1799 0.27-0.3599 0.36-0.4499 0.45-0.5399 0.54-0.6299

Midpoint	Frequency
0.04495	13
0.13495	75
0.22495	32
0.31495	23
0.40495	24
0.49495	11
0.58495	10
0.67495	4

Frequency polygon 80 70 60 50 40 Frequency 30 20 10 0 0 0.2 0.4 0.6 0.8

b)

No values are greater than 0.9. Hence, zero percent

c)

63 subjects had S/R values less than 0.70. i.e (63/192)= 0.3281

Therefore, 32.8125 percent had S/R in the range 0.3 - 0.699

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