Write your answers onto one or more separate sheets of paper. Clearly mark each sheet with your name and your lab time. Round all answers to at least 3 decimal places.
1. Below is a contingency table from a study that recorded the blood types of malaria patients at a clinic in India as well as those of a control group of people in the same region not infected with malaria:
Table 1 – Blood Types
A
B
O
AB
Malaria Cases
28
39
21
8
Control
41
110
85
14
a. What proportion of people in this study were infected with malaria? (1pt)
b. What is the probability that a malaria patient had blood type O? (1pt)
c. What proportion of the people in this study had blood type B and were not infected with malaria? (1pt)
d. Of the people with blood type A or AB, what proportion were infected with malaria? (2pt)
2. Create a sample of numbers with the following four properties. There are many possible correct answers for this question, so you need to show that each property is true for your sample. (4pt)
𝑛 = 7
Range = 20
The mean is less than the median
Mode = 100
3. Suppose a certain drug causes kidney damage in 12% of patients who take it. The drug is given to three patients, and the effect of the drug on each patient is independent of the others.
a. What is the probability that none of the patients will experience kidney damage? (3pt)
b. If the first two patients experience kidney damage, what is the probability that the third patient will not experience kidney damage? (2pt)
Copyright © 2016 Dept. of Statistics and Data Sciences, UT Austin
4. Desert lizards regulate their body temperature by moving between sunny and shaded areas. To see if a lizard’s body temperature affects their resistance to bacterial infection, scientists infected two different groups of lizards. One group of 20 lizards was put in an enclosure at a “normal” temperature (38°C) while another group of 15 lizards was kept in a “hot” enclosure (2-4°C hotter than normal). The following graph shows the survival rates of each group after 24 hours in the enclosures:
a. What are the variable(s) being displayed? For each variable, identify whether it is numeric or categorical. If numeric, is it discrete or continuous? If categorical, is it nominal or ordinal? (2pt)
b. How many of all the lizards in the experiment survived? (2pt)
c. Citing the appropriate statistics, briefly summarize what this graph shows in the context of what the scientists were investigating. (2pt)