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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
ME SEMESTER I EXAMINATION WINTER 2018
Subject Code: 2713107 Date: 11-Dec-2018
Subject Name: Statistics for Biomedical Engineers
Time: 10:30 AM To 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 Define random variable. Discuss various types of random variables and their properties. 07
Define below given terms with appropriate examples.
1. Null hypothesis 5. Type II error
2. Hypothesis test 6. p-value
3. Alternative hypothesis 7. Critical region
4. Type I error
07
Q.2 Explain pdf and cdf with necessary examples. 07
Below given table shows Ages of Patients in a Primary Care Medical Clinic of 50 Subjects.
i. Construct a frequency histogram and a cumulative frequency histogram using the
following class intervals: 10-19, 20-29, 30-39, 40-49, 50-59, 60-69, 70-79, 80-89, 90-
99, 100-109.
ii. Determine the lower and the upper quartiles and generate a box-and-whiskers plot for
the data.
iii. Construct a stem-and-leaf plot.
07
OR
Below given table shows Blood Levels of 50 Subjects.
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i. Construct a frequency table with nine intervals and then calculate the mean and median blood levels.
ii. Determine the lower and the upper quartiles and generate a box-and-whiskers plot for the data.
iii. Construct a stem-and-leaf plot.
Q.3

What is the difference between coefficient of variance and standard deviation? Which is more suitable measure of spread? Justify answer with example.
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Based on the following table of hemoglobin levels for miners, compute the probabilities described below. Assume that the proportion in each category for this set of 90 miners is the true proportion for the population of miners.
i. Compute the probability that a miner selected at random from the population has a hemoglobin level in the 12.0-17.9 range.
ii. Compute the probability that a miner selected at random from the population has a hemoglobin level in the 18.0-21.9 range.
iii. Compute the probability that a miner selected at random from the population has a hemoglobin level in the 22.0-27.9 range.
iv. What is the probability that a miner selected at random will have a hemoglobin count at or above 18.0?
v. What is the probability that a miner selected at random will have a hemoglobin count at or below 21.9?
vi. If two miners are selected at random from the "infinite population" of miners with the distribution for the miners in the table, what is the probability that one miner will fall in the lowest class and the other in the highest (i.e., one has a hemoglobin count in the 12.0 to 17.9 range and the other has a hemoglobin count in the 22.0 to 27.9 range)?
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OR
Q.3

Define estimation. Explain Binomial and Poisons distributions.
07

Data of weight-height of 10 persons is as shown in below given table. Find the value of correlation coefficient
ID
Weight
(pound)
Height
(inch)
ID
Weight
(pound)
Height
(inch)
ID
Weight
(pound)
Height
(inch)
1
148
64
5
110
63
9
153
66
2
172
63
6
134
62
10
170
64
3
203
67
7
195
59
4
109
60
8
147
62
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Q.4

Explain confidence intervals with necessary diagrams.
07

Below given table shows Body Mass Index Data for a Sample of 120 Adults: Ordered Array (Sorted in Ascending Order).
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Prepare a table and draw histogram graphs of below listed values for
mentioned seven intervals.
1. 18.0 20.9
2. 21.0 23.9
3. 24.0 26.9
4. 27.0 29.9
5. 30.0 32.9
6. 33.0 35.9
7. 36.0 38.9
1. Frequency f
2. Cumulative Frequency f
3. Relative Frequency
4. Cumulative Relative Frequency
OR
Q.4 Describe the Z and t statistics for two independent samples with necessary equations. 07
A study assessed the acute effects of alcohol on auditory brainstem potentials in humans. The
latency (delay) in response to an auditory stimulus was measured before and after an intoxicating
dose of alcohol of six volunteers. Measurements of the latency of peak (in milliseconds after the
stimulus onset) in the six subjects were as follows:
Test the significance of the difference at the 0.05 level.
Calculate the p-value associated with the result observed.
Is your p-value based on a one- or two-tailed test? Why?
Carry out an (incorrect) two-sample test and state your conclusions.
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Q.5 Describe the hypothesis test for a single binomial proportion with necessary equations. 07
Robinette et al. [1980] studied the effects on health of occupational exposure to micro-wave
radiation (radar). The study looked at groups of enlisted naval personnel who were enrolled
during the Korean War period. Find 95% confidence intervals for the percent of men dying of
various causes, as given in the data below. Deaths were recorded that occurred during 1950-
1974.
a. Eight of 1412 aviation electronics technicians died of malignant neoplasms.
b. Six of the 1412 aviation electronics technicians died of suicide, homicide, or other trauma.
c. Nineteen of 10,116 radar men died by suicide.
d. Sixteen of 3298 fire control technicians died of malignant neoplasms.
e. Three of 9253 radiomen died of infective and parasitic disease.
f. None of 1412 aviation electronics technicians died of infective and parasitic disease.
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OR
Q.5 Explain the mean and standard deviation for the binomial distribution with necessary graphs. 07
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Remein and Wilkerson [1961] considered a number of screening tests for diabetes. They had a group of consultants establish criteria, their gold standard, for diabetes. On each of a number of days, they recruited patients being seen in the outpatient department of the Boston City Hospital for reasons other than suspected diabetes. The table below presents results on the Folin-Wu blood test used 1 hour after a test meal and using a blood sugar level of 150 mg per 100 mL of blood sugar as a positive test.
i. Find sensitivity specificity.
ii. Find predictive value of a positive test predictive value of a negative test.
iii. Suppose that the prevalence of the disease was not 70/580 (as in the data given), but rather, 6%. Also suppose that the sensitivity and specificity of the test were same as earlier. What is the new predictive value of a positive test?
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