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UCLA Statistics, Neurology, LONI, Math/PIC

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STAT 13 (1a, 1b, 1c, 1d)	*Introduction to Statistical Methods for the Life and Health Science*
Department of Statistics	Instructor: Ivo Dinov
Homework 2	Due Date: Fri, Jan. 21, 2011

Please, submit your homework right before lecture on the due date. See the HW submission rules. On the front page include the following header.

(HW_2) Solve the following problems:

Suppose that in a certain population of married couples 30% of the husbands smoke, 18% 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?

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:

All 20 will be cured.
All but 1 will be cured.
Exactly 17 will be cured.
Exactly 80% will be cured.

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). Compute the following probabilities for a randomly chosen group of 16 children from this population:

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)

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 the Roulette 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?

Suppose that a long stretch of DNA has only Adenine (A), Thiamine (T), Cytosine (C) and Guanine (G) randomly occurring with the following probabilities 0.25, 0.3, 0.25, 0.2, respectively. The A, T, C and G nucleotides make up the core of the genetic code for any species. What is the probability that

A random drawing of 5 A's in a row in a sample of 6 randomly chosen nucleotides?
A random sample of 5 nucleotides has equal number of A's and T's?
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 calculations above.

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