Ams Homework
AMS 110.03 Homework #2 (100 Points, 10 per question) 1. Identify the variable(s), type(s), subtype(s), observational unit(s), and sample size(s) of the following settings.
Explain your reasoning if necessary. a. A paleontologist measured the width (in mm) of the last upper molar in 36 specimens of the extinct
mammal Acropithecus rigidus. b. The birthweight, date of birth, and mother’s race were recorded for each of 65 babies. c. A physician measured the height and weight of each of 37 children. d. During a blood drive, a blood bank offered to the check the cholesterol of anyone who donated blood. A
total of 129 persons donated blood. For each of them, the blood type and cholesterol levels were recorded.
e. A biologist measured the number of leaves on each of 25 plants.
2. A paleontologist measured the width (in mm) of the last upper molar in 36 specimens of the extinct mammal Acropithecus ridigus. The results were as follows:
6.1 5.7 6.0 6.5 6.0 5.7 6.1 5.8 5.9 6.1 6.2 6.0 6.3 6.2 6.1 6.2 6.0 5.7 6.2 5.8 5.7 6.3 6.2 5.7 6.2 6.1 5.9 6.5 5.4 6.7 5.9 6.1 5.9 5.9 6.1 6.1
a. Construct a frequency distribution and display it as a table and as a histogram. b. Describe the shape of the distribution based on its histogram.
3. The total amount of protein produced by a dairy cow can be estimated from periodic testing of her milk. The
following are the total annual protein production values (lb) for twenty-eight 2-year-old Holstein cows. Diet, milking procedures, and other conditions were the same for all the animals.
425 481 477 434 410 397 438 545 528 496 502 529 500 465 539 408 513 496 477 445 546 471 495 445 565 499 508 426
a. Construct a grouped frequency distribution and display it as a table and as a histogram. Each group
should have an interval length of 50. b. Describe the shape of the distribution based on its histogram.
4. In a study of schizophrenia, researchers measured the activity of the enzyme monoamine oxidase (MAO) in the
blood platelets of 18 patients. The results (expressed as nmoles benzylaldehyde product per 108 platelets) were as follows:
6.8 8.4 8.7 11.9 14.2 18.8 9.9 4.1 9.7 12.7 5.2 7.8 7.8 7.4 7.3 10.6 14.5 10.7
a. Determine the median and the quartiles. b. Determine the interquartile range. c. How large would an observation in this data set have to be in order to be an outlier? How small? d. Construct a box plot of the data. (Include the upper fence and lower fence)
5. In a certain population of the freshwater sculpin, Cottus rotheus, the distribution of the number of tail vertebrae is shown in the table.
Number of Vertebrae Percent of Fish
20 3
21 51
22 40
23 6
Total 100
Find the probability that the number of tail vertebrae in a fish randomly chosen from the population:
a. Equals 21
b. Is less than or equal to 22
c. Is greater than 21
d. Is no more than 21
6. In a study of the relationship between health risk and income, a large group of people living in Massachusetts were asked a series of questions. Some of the results are shown in the following table.
Income
Low Medium High Total
Smoke 634 332 247 1213
Don’t smoke 1846 1622 1868 5336
Total 2480 1954 2115 6549
a. What is the probability that someone in this study smokes? b. What is the conditional probability that someone in this study smokes given that the person has high
income? c. Is being a smoker independent of having a high income? Why or why not? d. What is the probability that someone in this study is not from the low income group? e. What is the probability that someone in this study is from the low income group or from the medium
income group? 7. Suppose that in a certain population of married couples, 30% of the husbands smoke, 20% of the wives smoke,
and in 8% of the couples both the husband and wife smoke. Is the smoking status (smoker and nonsmoker) of the husband independent of that of the wife? Why or why not?
8. Suppose that a disease is inherited via a sex-linked mode of inheritance, so that a male offspring has a 50% chance of inheriting the disease, but a female offspring has no chance of inheriting the disease. Further suppose that 51.3% of the births are male. What is the probability that a randomly chosen child will be affected by the disease?
9. In a particular pain clinic, 10% of patients are prescribed narcotic pain killers. Overall, five percent of the clinic’s
patients are addicted to narcotics (including pain killers and illegal substances). Out of all the people prescribed pain pills, 8% are addicts. If a patient is an addict, what is the probability that they will be prescribed pain pills?
10. Suppose that a medical test has a 92% chance of detecting a disease if the person has it (i.e. 92% sensitivity) and a
94% chance of correctly indicating that the disease is absent if the person really does not have it (i.e. 94% specificity). Suppose 10% of the population has the disease.
a. What is the probability that a randomly chosen person will test positive?
b. Suppose that a randomly chosen person does test positive. What is the probability that this person really
has the disease?