Part I(short essay/discussion)
#1: Why do so many Americans struggle with mathematics/statistics? I have always believed that learning mathematics is similar to learning a foreign language. There are certain rules that you must learn and there are exceptions to the rules. You then have to use your logic. How to use logic is a process learned through practice.
I assume that most of you took a course in geometry when you were in high school. I seldom got to teach geometry in the 70’s. As a department head for a mathematics team of 10 teachers, I wanted my teachers to select the classes they preferred to teach. That left me to teach Pre-Calculus, Calculus, Linear Algebra, Computer Math, Statistics and remedial math for our struggling students. Luckily, I loved teaching all of these courses.
This is how I taught geometry. I used my classroom – the floors, the walls, the lines separating the walls. I started with what information we knew and what we wanted to prove – how do we get from point A to point B. We had to logically think this process out. Unfortunately, many students just memorized the steps. If the teacher then changed the information given, the steps we memorized no longer worked. What are your thoughts?
#2: What is the importance of statistics in Professional and Personal Life?
4.) To estimate the percentage of households in Connecticut which use fuel oil as a
heating source, a researcher collects information from 1000 Connecticut
households about what fuel is their heating source. State the individual, variable,
population, sample, parameter, and statistic.
8.) The World Health Organization wishes to estimate the mean density of people per
square kilometer, they collect data on 56 countries. State the individual, variable,
population, sample, parameter, and statistic
4.) You wish to determine the GPA of students at your school. Describe what
process you would go through to collect a sample if you use a stratified sample.
4.) To evaluate whether a new fertilizer improves plant growth more than the old
fertilizer, the fertilizer developer gives some plants the new fertilizer and others
the old fertilizer. Is this an observation or an experiment? Why?
10.) A mathematics instructor wants to see if a computer homework system improves
the scores of the students in the class. The instructor teaches two different
sections of the same course. One section utilizes the computer homework system
and the other section completes homework with paper and pencil. Are the two
samples matched pairs or not? Why or why not?
16.) To determine if a new medication reduces headache pain, some patients are given
the new medication and others are given a placebo. Neither the researchers nor
the patients know who is taking the real medication and who is taking the placebo.
Is this a blind experiment, double blind experiment, or neither? Why?
2.) Suppose a car dealership offers a low interest rate and a longer payoff period to
customers or a high interest rate and a shorter payoff period to customers, and
most customers choose the low interest rate and longer payoff period, does that
mean that most customers want a lower interest rate? Explain.
8.) Suppose a telephone poll is conducted by contacting U.S. citizens via landlines
about their view of gay marriage. Suppose over 50% of those called do not
support gay marriage. Does that mean that you can say over 50% of all people in
the U.S. do not support gay marriage? Explain.
14.) An employee survey says, “Employees at this institution are very satisfied with
working here. Please rate your satisfaction with the institution.” Discuss how
this question could create bias.
4.) In Connecticut households use gas, fuel oil, or electricity as a heating source.
Table #2.1.7 shows the percentage of households that use one of these as their
principle heating sources (“Electricity usage,” 2013), (“Fuel oil usage,” 2013),
(“Gas usage,” 2013). Create a bar chart and pie chart of this data. State any
findings you see from the graphs.
Table #2.1.7: Data of Household Heating Sources
Heating Source Percentage
Fuel Oil 46.3%