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Introductory Probability and
Statistics
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The following are problems that could be
used in an Intro. Prob. and Statistics course, depending on what material the
class has covered. Therefore, problems are designed for different points in the
curriculum. The topic for each problem is given.
(Linear Regression)
1. The buying power of CUNY Library
Material Funds is given as follows:
$15.1 million $10 million $8.6 million
1990
1995
2000
Reduced funding means fewer resources
for CUNY’s students to use for learning.
Using this data, find the line of best fit (regression line) that
represents the trend of this data. If
this trend continues, what will be the funding for CUNY’s Library materials in
2005? How do you think that will
affect the average CUNY student experience?
Data for similar linear regression
problems:
1i – The number of Full-time Equivalent (FTE) students has been growing at CUNY in recent years and the numbers are given below. Find the line of best fit that represents this data. If this trend continues, how many students will be attending CUNY in 2007?
Compare the trend of this data with
those of the Library Materials. How
will these two trend interact? How
will this affect CUNY’s students in their pursuit for a quality education?
FTE Students: 146,412 142,493 145,728
Year:
1981
1990
1998
1ii – The Ratio of FTE students to
full-time faculty for CUNY is given below.
These numbers can be interpreted as the number of students per Full-time
faculty member. For example, in
1981, for every full-time faculty member, there were 19.8 (about 20) students.
Ratio of Students to Faculty: 19.8 21.9 27.8
Year: 1981 1990 1998
Find the line of best fit that
represents the trend in enrollment at CUNY.
If this trend continues, how many students will be attending CUNY in
2005? Compare this with the buying
power of CUNY Library Material Funds. How
will these two trends interact? What
affect will it have for CUNY’s students?
(Correlation Coefficient)
2. The number of full-time faculty at
CUNY and the FTE (full-time equivalent) student enrollment are given below:
Year:
1981
1990
1997-98
Faculty: 6,886 6,515 5,244
Students:
136,412
142,493
145,728
a) Graph these two sets of data together on the same set of axes. What can you say about their relationship?
b) Find the linear correlation
coefficient, r, for number of faculty to number of students over the years.
Is it positive or negative? Are
these numbers negatively or positively correlated? How do you think this affects the quality of education for
the average CUNY student?
3. (Binomial Probability)
In 1999, 56.8% of faculty at CUNY were part-time, while 43.2% were full-time. The part-time faculty are also know as adjunct faculty and are paid at a very low rate and are not paid for holding office hours for students. For the average CUNY student taking 5 classes, find the following probabilities:
a) Probability all of the 5 classes are taught by full-time faculty. Do you consider this probability high or low?
b) Probability 3 of the classes are taught by full-time faculty.
c) Probability that at least three of the classes are taught by full-time faculty.
d)
How do you think being taught by adjunct faculty rather than full-time
faculty affects the learning process for CUNY students?
What are some of the other outcomes that can happen in a school that has
more adjunct faculty than full-time faculty?
Data for similar Binomial Probability
Problems:
The chart below may be used for exactly the same types of problems as given in #3:
4. Using the information on the chart below, find the exponential regression model for the number of Full-time Faculty at CUNY. If this trend continues, what will be the number of full-time faculty in 2005, 2010? How will this affect a student’s education at CUNY?
submitted by Laurel Cooley, York College