HW 3 Complete Statistics
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Political Science
Date
Dec 6, 2023
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POLS 3316. Statistics for Political Science
Dr. Scott Basinger
Homework Assignment #3
Distributed Tuesday, September 19
Due Tuesday, September 26
1.
The Flesch-Kincaid score is designed to indicate how easy a passage in English is to understand. It was
developed for the U.S. Navy in 1975. The Grade-Level Score uses the average number of words per sentence
and the average number of syllables per word to determine at what grade level a text is written.
1
The second column of the table below shows Flesch-Kincaid scores for the last 14 presidents, based on all
presidential remarks in unscripted settings (i.e., press conferences, gaggles, and interviews) through their
first 2½ years in office. These data are posted as
readability.csv
. Use these data to:
A)
Calculate the median grade level of presidential remarks:
M =
B)
Calculate the first and third quartiles of presidential remarks:
Q1 =
Q3 =
C)
Calculate the interquartile range of presidential remarks
IQR =
D)
Calculate the mean grade level of presidential remarks
𝑥𝑥̅
=
E)
Fill in the table below and calculate the sum of squared deviations…
SS =
… and the variance
s
2
=
F)
Calculate the standard deviation of presidential remarks
s
=
G)
If a variable is distributed roughly Normally, then the ratio (IQR
÷
s
)
should be approximately equal to 1.35. Calculate this ratio:
IQR/
s
=
Presidents
i
Grade levels
𝑥𝑥
𝑖𝑖
Deviations from Mean
(
𝑥𝑥
𝑖𝑖
−
µ
)
Squared Deviations from Mean
(
𝑥𝑥
𝑖𝑖
−
µ
)
2
Bush 41
7.4
Bush 43
8.1
Carter
9.9
Clinton
9.0
Eisenhower
9.3
Ford
9.5
Johnson
8.5
Kennedy
9.6
Nixon
10.3
Obama
8.7
Reagan
8.5
Roosevelt
8.1
Truman
6.2
Trump
4.5
Sum
(
∑ ∎
)
SS =
Average
(
∑ ∎
)
𝑛𝑛
𝑥𝑥̅
=
Variance
(
∑ ∎
)
𝑛𝑛−1
s
2
=
The Flesch-Kincaid Grade Level Formula is:
2. According to the
Golf Channel
,
2
the time that elapses while waiting for a PGA Tour golfer to play a stroke has a
mean of
µ
≈
38 seconds and standard deviation
σ
≈
9 seconds. The PGA Tour maintains a 40-second time limit to
play a stroke, but has several exceptions that allow for an additional 20 seconds. However, if a player exceeds 60
seconds, a penalty stroke is assessed.
Assume that times are approximately Normally distributed. Find the standardized scores associated with each of
the following thresholds, and then use the Standard Normal Table (or the
pnorm
command in R) to find the
cumulative percentage associated with each value:
standardized score
percent below
a.
x = 40
z =
b.
x = 60
z =
3. Based on the “percent below” calculations in problem 2, you can calculate the following:
_______% of golf shots take 40 seconds or less
_______% of golf shots take between 40 and 60 seconds
_______% of golf shots take 60 seconds or more
4. The bell-shaped curve shown below illustrates a Standard Normal Distribution. Vertical lines have been drawn
for every ½ standard deviation away from the mean. Illustrate the calculations you performed in question 3:
[a] draw a vertical line that divides “40 seconds or less” from “more than 40 seconds”
[b] draw
a vertical line that divides “60 seconds or less” from “more than 60 seconds”
[c] lightly shade the area representing “between 40 and 60 seconds,” and
[d] darkly shade the area representing “more than 60 seconds.”
2
R. Hoggard, “PGA Tour Tracks Pace of Play,”
GolfTalkCentral
,
http://www.golfchannel.com/news/golftalkcentral/pga-tour-
trackspace-of-play
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