Hw #3 – STAT 110 ~ Numerical Summary Statistics (Due Tuesday, May 17th)
1.) A random sample n = 9 of duck nests in Mississippi Wildlife Refuge yielded the
following data for the number eggs in the nest:
13 11
8 6
6
4
7
9 10
a) Find the sample mean (2 pts.)
b) Find the sample median (2 pts.)
c) Find the sample mode (1 pt.)
d) Find the sample variance and sample standard deviation (6 pts.)
2.) Cigar Smoking and Cancer Death
The Journal of the National Cancer Institute (Feb. 16, 2000) published the results of a
study that investigated the association between cigar smoking and death from tobaccorelated cancers. Data were obtained for a national sample of 137,243 American men.
The results are summarized in the table below. Each male in the study was classified
according to his cigar-smoking status and whether or not he died from a tobacco-related
cancer. (16 pts. – 2 pts. each)
Cigars
Never Smoked
Former Smoker
Current Smoker
Column Totals
Yes
782
91
141
1,014
Died from Cancer
No
120,747
7,757
7,725
136,229
Row Totals
121,529
7,848
7,866
137,243
a) Find the probability that a randomly selected man never smoked cigars and died from
cancer.
b) Find the probability that a randomly selected man was a former cigar smoker and died
from cancer.
c) Find the probability that a randomly selected man was current cigar and died from
cancer.
d) Given that a male was current cigar smoker, find the probability that he died from
cancer.
e) Given that a male never smoked cigars, find the probability that he died from cancer.
f) How many times more likely to die from cancer is a male who is a current cigar
smoker than a male who has never smoked cigars.
g) How many times more likely to die from cancer is a male who is a former cigar
smoker than a male who has never smoked cigars.
h) Do the results from parts (f) and (g) prove that cigar smoking causes cancer? Explain.
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3. Bias in Graduate School Admissions at Univ. of Calif. – Berkeley
Bickel and O’Connell (1975) investigated whether there was any evidence of gender bias
in graduate admission at the University of California at Berkeley. The data file Berkeley
Sex Discrim 1975 contains the results of a cross-classification of 4,526 applicants to six
of the largest graduate programs in 1973 by Sex (M or F) and Admission (whether or not
the applicant was admitted to the program to which they applied).
a) What percent of male applicants were admitted to these programs? What percent of
female applicants were admitted? What percent of all applicants were admitted? Does
there appear to be any sexual discrimination in graduate school admissions, i.e. are sex
and admission related? (4 pts.)
b) Now consider a cross-classification of sex and admission for each of these six
programs individually. Do these indicate any sex discrimination in admissions? Explain
and justify your conclusions. (4 pts.)
Program A
Program B
Program C
Program D
Program E
Program F
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