Exercises_BIOSTATISTICS - Exercises on BIOSTATISTICS I...

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1 Exercises on BIOSTATISTICS I. Introduction to descriptive statistics 1. Consider the “body length of a student who follows the course biostatistics” as continuous random variable. Construct the frequency distribution and define the classes such that they all contain about 5 outcomes. Construct the bar graph and histogram. Compute the mean height in 2 ways: i) using the individual heights and ii) using the classes (class frequencies and class centers). Do the two results agree perfectly? Why? 2. Consider the “Degree or certificate last obtained” as a non-quantitative random variable. Display the results in a pie chart (Small sectors shall be grouped into a sector “other” such that the total number of sectors amounts to about 6). 3. The voltage of a battery is measured repeatedly. One obtains consecutively: 1.65 V, 1.48 V, 1.71 V, 1.45 V, 1.79 V, 1.71 V. Calculate the mean, median, modus, standard deviation of the sample, variance and coefficient of variation. Knowing that the real voltage amounts to 1.5 V, do you expect the errors to be random or systematic? [ Answer: m x = 1.63 V, median = 1.68 V, modus = 1.71 V, s = 0.14 V, s 2 = 0.019 V 2 , vc=0.085 ] 4. After measuring the blood pressure of a group of selected patients, the physician calculates a mean of 12 cm Hg and a standard deviation of 2 cm. Suddenly, the physician detects a systematic error: the sphygmomanometer has indicated too low by 1 cm. How will the physician correct the mean, the standard deviation and the coefficient of variation (without measuring again)? II. Basics of probability 1. Do you agree with the following reasoning: “I have won the Lottery today. Now, I will stop gambling since my chances have shrunk away. The probability of winning two times a year is extremely low”. Explain. 2. Consider a family that has 4 children. Assume that the probability for a son equals 0.51. What is the probability that the family has 0, 1, 2, 3 and 4 boys? Make the sum of the probabilities found. 3. The probability for exposure to influenza during an epidemic amounts to 0.6. There is a serum on the market that protects the vaccinated person for 80% when exposed. A person who has not been vaccinated, however, has a probability of being infected of 0.9 when exposed. We randomly consider two persons, one is vaccinated and the other is not. What is the probability that at least one of the two will catch influenza? 4. A radiation therapist has set up a frequency distribution of the total radiation dose delivered to his patients. He used the obsolete unit rad . He has computed the following parameters: mean, standard deviation, variance, coefficient of variation, quartiles, skewness and kurtosis. Now he wants to present his data expressed in the unit Gy = 100 rad . In which way the therapist has to adapt the numerical values of his parameters?
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2 5. In medicine, it often happens that a number of diseases cause the same symptoms. Assume that a given symptom, which we call event H, can only occur as a consequence of 3 possible underlying diseases A, B and C (mutually exclusive). A study has shown that P(A) = 0.01, P(B) = 0.005, P(C) = 0.02, P(H|A) = 0.90, P(H|B) = 0.95 en P(H|C) = 0.75. Which is the probability that
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