6 Problems on Homework 2 - Applied Statistics for the Life Sciences | STAT 371, Assignments of Statistics

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Stat 371 Homework #2 Due Th. Feb. 2, 2006

This homework assignment covers the end of chapter 2 and part of Chapter 3.

1. Exercises from chapter 2: 2.50, 2.51, 2.54 and 2.80.
2. Some of the survey’s results are available from the course web site. You will find a short version containing 12 individuals only, and a complete version containing all individuals. Both files report results from the following variables: “Miles-from-Home”, “Height” and “Number”. Data are exactly as you entered them. The only exception is when a student didn’t answer a question. In that case, the file shows “NA”, meaning “not available”. This gives you an opportunity to see what kinds of issue arise with real data, that might not always look like what we expect. You might have to make decisions... You can use anyone of the 2 data sets. If you plan to do calculations with your calculator, I suggest that you use the small data set (short version). If you plan to use R, you can use the complete data set easily, because you don’t need to type in any data. At this point, I don’t assume that you know R, and using R is not a requirement.

(a) Construct a boxplot of the miles-from-home data. (b) Calculate the mean and the standard deviation of the variable “Height”. Any com- ment? What do you think could have happened if you had entered your height in feet and inches? (c) Make a histogram of the variable “Number”.

3. Exercise 3.2 from the textbook. Make sure you use an objective way to do the sampling! Your own judgment might not be objective. You may use table 1 from the text (see the text for instructions), or your calculator. With R, use the command sample(0:99,5) to build one sample of size 5, drawn from the set 0, 1 , 2 ,... , 98 , 99. Here are additional questions.

(a) Let Y be the number of mutants observed among 5 individuals from the population C.ellipticus. You got 10 observations y 1 ,... , y 10. Construct a histogram of these data. (b) Calculate the mean of your 10 values y 1 ,... , y 10. (c) Keep your results for future use in discussion.

4. Exercise 3.13. Question (d) should be: What is the probability that someone in this study is stressed and has low income? Additionally, determine whether being stressed is independent of having low income, in the sample.
5. Exercise 3.15. Also determine where the median of the distribution is, approximately. Determine its shape (bell shaped? skewed? if so, to what side? more than one mode?).
6. Let Y be a number chosen at random between 0 and 9. Draw the table describing the distribution of Y and draw its histogram. Does it look like the histogram drawn in (2c)?

Reading:

• Chapter 3: sections 1 to 8.

C´ecile An´e