## STAT 13

(Sec. 1a-1c)

Introduction to Statistical Methods for the Life and Health Sciences

## Instructor: Ivo Dinov, Asst. Prof.

Departments of Statistics & Neurology
 http://www.stat.ucla.edu/~dinov/

Due Date:

# Monday, Oct. 29, 2001, turn in after lecture

See the HW submission rules. On the front page include the following header.

• (HW_4_1) A landscape designer is designing a large garden for a new home. The client is particularly fond of palms and would like to have them included. The landscape designer knows that in the local climate, palms are given only a 30% chance of surviving the first year. Generally, if the palms survive the first year, they will continue to flourish. The landscape designer is considering a design which includes a random sample of 11 palms (not from the same root stock). Let X be the number of palms that survive the first year after planting.
• Discuss the validity of using the Binomial distribution in this situation. (Hint: consider the conditions for this distribution and consider how well these conditions are satisfied here).
• State the value of the parameter(s) of this distribution.
• Assuming that the distribution you have described above is an appropriate model for X, find the probability that:
• no more than 3 of the palms survive the first year.
• only 1 of the palms survive the first year.
• between 2 and 6 palms (inclusive) survive the first year.
• How many palms would you expect to survive the first year? What is the standard deviation of X?

• (HW_4_2) A medical trial was conducted to investigate whether a new drug extended the life of patients who had lung cancer. The survival times (in months) for 38 cancer patients who were treated with the drug are as follows:
•  1 1 5 9 10 13 14 17 18 18 19 21 22 25 25 25 26 27 29 36 38 39 39 40 41 41 43 44 44 45 46 46 49 50 50 54 54 59
Sample mean ~= 31.1 months and standard deviation ~=  16.0 months.
• Assume that the survival time (in months) for patients on this drug is Normally distributed with a mean of 31.1 months and a standard deviation of 16.0 months.
• What is the probability that a patient survives for no more than one year?
• What proportion of patients will survive between one year and two years?
• What is the highest survival time that 80% of patient survival times exceed?
• Calculate the central 80% of survival times.
• Draw a stem-and-leaf plot of the number of months of survival for these 38 patients.
• Does the plot give us any reason to question the assumption that the survival times are Normally distributed?

\Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology, UCLA School of Medicine/