|STAT 13 (1a,
1b, 1c, 1d)
Methods for the Life and Health Science
|Department of Statistics
Instructor: Ivo Dinov
|Due Date: Fri, Feb. 03, 2012
- (HW2.1) Suppose that in a
certain population of married couples 35% of the
husbands smoke, 15% of the wives smoke and in 10% of the couples both
the husband and wife smoke. Is the smoking status of the husband
independent of that of the wife? Why or why not?
- (HW2.2) A certain drug
treatment cures 90% of cases of hookworm in
children. Suppose that 20 children
suffering from hookworm are to be treated, and that the children can be
regarded as a random sample from the population. Find
the probability that:
will be cured.
but 1 will be cured.
- Exactly 17 will be cured.
80% will be cured.
- (HW2.3) Childhood lead
poisoning is a public health concern in the US. In a certain
population, one child in seven
has a high blood lead level (>30 µg/dLi).
following probabilities for a randomly chosen group of 16 children from
- P(none have high blood lead)
- P(one has high blood lead)
- P(two have high blood lead)
- P(three or more have high blood lead)
- (HW2.4) Use the SOCR
Roulette Experiment to design and run a simulation estimating the
probability that a number between 19 and 36 turns up is we spin
Wheel. Compute the exact
probability of this event and list the sample-driven estimates of this
event for samples of size 10, 100 and 1,000. What is your
observation about these probability estimates?
- (HW2.5) Suppose that a
long stretch of DNA has only Adenine (A),
Thiamine (T), Cytosine (C) and Guanine (G) randomly occurring with the
following probabilities 0.20, 0.3, 0.25, 0.25, respectively. The A, T, C and G nucleotides make
up the core of the genetic code for any species. What is the
- A sample of 6
randomly chosen nucleotides contains 5 A's in a row?
- A random sample of 5 nucleotides has equal number of A's and
- Use the SOCR
Spinner experiment (remember to set the right number of sectors, 4,
and correct probabilities) to simulate the situations above and find
empirical answers to the first 2 questions. Run 100 simulations and
compare the empirical results of the applet with your theoretical