Problem 35RE
Age and party 2011 II Consider again the Pew Research Center results on age and political party in Exercise.
a) What is the marginal distribution of party affiliation?
b) Create segmented bar graphs displaying the conditional distribution of party affiliation for each age group.
c) Summarize these poll results in a few sentences that might appear in a newspaper article about party affiliation in the United States.
d) Do you think party affiliation is independent of the voter’s age? Explain.
Exercise
Age and party 2011 The Pew Research Center conducts surveys regularly asking respondents which political party they identify with or lean toward. Among their results is the following table relating preferred political party and age. (http://peoplepress.org/)
Party  

Republican/Lean Rep. 
Democrat/Lean Dem. 
Neither 
Total 

Age 
18–29 
318 
424 
73 
815 
30–49 
991 
1058 
203 
2252 

50–64 
1260 
1407 
264 
2931 

65+ 
1136 
1087 
193 
2416 

Total 
3705 
3976 
733 
8414 
a) What percent of people surveyed were Republicans or leaned Republican?
b) Do you think this might be a reasonable estimate of the percentage of all voters who are Republicans or lean Republicans? Explain.
c) What percent of people surveyed were under 30 or over 65?
d) What percent of people were classified as “Neither” and under the age of 30?
e) What percent of the people classified as “Neither” were under 30?
f) What percent of people under 30 were classified as “Neither”?
Calculus I Chapters 1.1 and 1.2 Chapter 1.1 – An Introduction to Calculus Formulas to remember 2 2 o ( − + = − o ( + )2 = + 2 + 2 2 2 2 o ( − ) = − 2 − −± −4 o = 2 1.1 Preview of Calculus Calculus is the mathematics of change PreCal Cal Δ Slope = Δ Area Of rectangle = ℎ 2) the Tangent Line Problem Finding a tangent line to a curve @ point P is equivalent to finding the slope of the tangent line at P.  We will use the secant line: a line through the point P of the tangent and a point Q also on the curve. ( ) 2 For = = 1 = 1 2 1.1 = 1.1 = 1.21 1(1.1, 1.1 ) = 1.1,1.21 ) (1.5 , 1.5 ) = (1.5,2.25) 2 3(1.01, 1.01 ) = 1.01,1.0201 ) (1.001, 1.001 ) = 1.001,1.002 ) 4 Slope of P, Q + ∆ − ) + ∆ − ) = = ( + ∆ − ∆ = 1 ∆ = 1 − 1.1 = 0.1 1 + 0.1 − 1) 1 = 0.1 1.1 − 1) 1.21 − 1 0.21 = = = = 2.1 1 0.1 0.1 0.1 1.01 − 1 ) 3 = 0.01 1.0201 − 1 0.0201 3 = 0.01 = 0.01 = 2.01 1.001 − 1 ) 4 = 0.001 1.002 − 1 0.002 4 = = = 2 0.001 0.001 2 = − 1 : = 1 − 1 0 = 1, 1 = , −1 = 1 = , = 2 + 1 ( ) = 2 + 1 )2= 4 + 4 + 4 ( ) = 2 + 1 Chapter 1.2 Finding Limits Graphically and Numerically 1) The informal definition of a limit a. b. ℎ c. If () becomes extremely close to the number and approaches from either side, then we say: ℎ ,ℎ . And we write graphically → = Ex: = −2 = −2 = 1 = 2 −4 (+2)(−2) +2 1 lim = →2 4 lim = →−2 Numerically: 1.9 1.99 1.999 2 2.001 2.01 2.1 () 0.256 0.251 0.250 0.25 0.2499 0.2494 0.2439 2) Learning and using the formal definition of a limit → = This means that for each > 0, there exists a > 0 If 0 < − < , then  −  < and are positive numbers 0 < − < either is in the interval ( − , + ) or is in ( − , or ( + ,) Ex: using the term and definition = + 2 = 4 Lim + 2 = 6 →4 Find that satisfies: 0 < − < implies − < ( )   − 6 = + 2 − =  − 4 If we want − 4 < 3, must choose ) 3) Learn different ways that a limit can fail to exist I) Behavior that differs from the left and the right YValues 2.5 2 1.5 1 0.5 0 3 2 1 0 1 2 3 4 5 0.5 1 1.5 2 2.5 II) Unbounded behavior III) Oscillating behavior = sin( )1 1 lim sin( ) = →0