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Spring 2002: STAT 3000_
Homework assignment 3
Due Wednesday, January 30, 2002
NAME: __________________________
Work on the homework individually or in groups (encouraged - but remember: every person has to turn in his/her individual assignment sheet). Attach as many sheets of paper as you need. Show your work wherever possible for full credit.
You may use your calculator or a computer software for all problems in which is not specifically indicated that you should work "by hand". If you use computer software, please indicate which software you have used and include the original printout wherever possible.
Number of points you get for each problem is given in parentheses. You can get a maximum of 30 points for this homework.
I (9 pts) Please work on the following problems from Chapter 6 of the Hayter book:
6.3.1, 6.3.2, 6.3.3 ( 3 pts each)
Please solve these problems "by hand" and with help of your hand calculator. Always write down the formula you are using.
II (6 pts) For this problem you will use the data we collected in the class (handout). You can also download the data from the STAT 3000 Web page:
Excel file: http://www.math.usu.edu/~vukasino/teaching/spring2002/stat3000/Data/student_data.xls
Text file: http://www.math.usu.edu/~vukasino/teaching/spring2002/stat3000/Data/student_data.txt
Solve these problems using computer software or your calculator. Do not exclude any observation. If you find an outlier, explain in one or two sentences how this observation influences your sample statistics.
a) (3 pts) Calculate mean, 10%-trimmed mean, median, and mode of the height of the male students. Which one do you prefer to describe the center of the distribution?
b) (3 pts) Calculate range, variance, and standard deviation of the height of the male students.
2
III (15 pts) The following problem has been taken from the first Midterm exam in Spring 2000:
The table below shows summary statistics (obtained using Microsoft Excel's Data Analysis Toolpack and the built-in statistical function 'QUARTILE') of survival times in days of 72 guinea pigs after they were injected with tubercle bacilli in a medical experiment (data from T. Bjerkedal, "Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli", American Journal of Hygiene , 72 (1960), pp. 130 - 148; data not shown).
Survival time in days
Mean 141. Standard Error 12. Median 102.5 Upper quartile: 149. Mode 81 Lower quartile: 82. Standard Deviation 109.2086335 IQR: 66. Sample Variance 11926. Kurtosis 6. Skewness 2. Range 555 Minimum 43 Maximum 598 Sum 10213 Count 72
Look carefully at these summary statistics and then answer the following questions:
a) (3 pts) What can you conclude about the center of the distribution of survival times by looking at mean , median , and mode of the data? Explain your answer in one or two sentences.
b) (4 pts) What information about the distribution of survival times can you get by looking at the quartiles, interquartile range, and min and max of the data (it might be helpful to sketch a box plot here).
c) (4 pts) Which measures would you use to describe the spread of the distribution of survival times - variance and standard deviation or quartiles and interquartile range (along with min and max)? Write a sentence or two to explain your answer.
d) (4 pts) What do kurtosis and skewness tell you about the shape of the distribution of survival times? Explain your answer in a sentence or two. Draw a rough sketch of the distribution of survival times.
