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Statistics
1.
Yue
Assignment #2, Due 2009/11/03
Oct. 20, 2009
According to a salary survey conducted by the Council of Labor Affairs,
Executive Yuan, Taiwan, the average monthly salary of workers in the
manufacturing sector is NT$39,583 (Yearbook of Labor Statistics, Taiwan:
2003). The following is a sample of the monthly salaries in hundreds of NT$.
43.9
32.9
40.2
42.0
42.1
43.2
42.0
43.9
41.5
40.8
38.2
42.6
42.3
39.8
37.9
41.8
42.0
39.7
38.9
38.8
39.2
36.8
37.3
41.9
39.9
32.7
33.6
44.2
32.0
42.4
(a) What are the mean, median, mode, first quartile, and third quartile?
(b) What are the range, interquartile range, variance, and coefficient of variation?
2.
Use the random number generator in Minitab to generate observations.
Generate 100 observations each from U(0,10), N(5,16), and Exp(5).
(a) Using these data to check the validity of Chebyshev’s theorem.
(b) Check if the data satisfy the empirical rule and give your interpretation.
(c) Measure the skewness of these three data sets.
3.
Do students with higher IQ test scores tend to do better in school? You need
to go to my web page and download the data set of IQ and student grade
point average (GPA) for 78 seventh-grade students in a rural Midwest school.
(a) Draw a scatterplot of IQ and GPA for these 78 students, and state in your
opinion if there exists a positive association between IA and GPA.
(b) What is the form of the relationship between IQ and GPA? Is it roughly
linear? Is it very strong? Explain your answers.
(c) At the bottom of the plot are several points that we might call outliers, i.e.
observations that are “different.” Judge in your opinion how many outliers
are there.
4.
The Pick 4 games in many state lotteries announce a four-digit winning
number each day. The winning number is essentially a four-digit group from
a table of random digits. You win if your choice matches the winning digits.
Suppose your chosen number is 5168.
(a) What is the probability that your number matches the winning number?
(b) What is the probability that your number matches the digits in the winning
number in any order?
5.
The following table shows the distribution of blood types in the general
population (Hoxworth Blood Center, Cincinnati, Ohio, March 26, 2003).
A
B
AB O
Rh+ 34% 9% 4% 38%
Rh- 6% 2% 1% 6%
.
(a) What is the probability a person will have type O blood?
(b) What is the probability a person will be Rh+?
(c) What is the probability a married couple will both be Rh+?
(d) What is the probability a married couple will both have type AB blood?
(e) What is the probability a person will be Rh+ given she or he has type O blood?
(f) What is the probability a person will have type B blood given he or she is Rh+?
6.
A patient takes a lab test and the result comes back either positive or negative.
The test returns a correct positive result in 99% of the cases in which the
disease is actually present, and a correct negative result in 98% of the cases
in which the disease is not present. Furthermore, .001 of all people have this
cancer.
(a) If a person is tested positive, what is the probability that this person has the
cancer.
(b) If a person takes two independent tests and both return positive results. What
is the probability that this person has the cancer?
(c) If a person takes two independent tests and only one returns positive result.
What is the probability that this person has the cancer?