Distribution of the Sample
Proportion Name: __________
Remember the worksheet for which you rolled
dice? The point of the worksheet was to
examine the sampling distribution of the sample mean. That’s why I had you generate several samples
(of dice rolls) and calculate the sample mean for each sample – so we could see
how these sample means vary. Now I want
to do the same thing for a different statistic: the sample proportion. So I want you to generate several samples (of
coin spins this time), and calculate the sample proportion (of heads) in each
sample – so we can see how these sample proportions vary. Get ready for more tedium!
First, I want to make sure you understand the
spinning process. You must give the
penny lots of rotational momentum, and it must come to rest without hitting
anything. The former requires that you
don’t just give the coin a little twist with your wrist, but that you hold the
penny on edge with one finger and flick it with your other finger – as if
place-kicking a football, sort of. The
latter requires a large, flat, hard surface.
If the penny hits anything before coming to rest, disregard that
attempt.
Believe it or not, pennies spun in this fashion are
not equally likely to land heads up and tails up. I’ll explain why after we collect the
data. Please use a penny from the
1960’s; 1961 and 1962 are ideal to bring out this effect. Record the year of the penny that you use:
______
For now, I’d like you to generate three samples of
10 spins each, and three samples of 20 spins each. Then calculate the proportion of heads in
each of those samples. (The sample
proportions should be multiples of 0.1 in the samples of 10, and multiples of
0.05 in the samples of 20.)
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spin: |
1 |
2 |
3 |
4 |
5 |
6 |
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8 |
9 |
10 |
prop. of H’s |
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sample 1 |
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sample 2 |
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sample 3 |
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spin: |
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20 |
prop. H’s |
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sample3 |
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Last but not least, I want you to draw three random
samples of 20 students from the 1995 Witt New Student population, listed on the
back of this sheet, and record the proportion of students from Ohio in each of
your three samples. (Be sure to use
three-digit numbers in your randomization.)
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proportion from Ohio |
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sample 1 |
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sample 2 |
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sample 3 |
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001 IN
002 OH
003 IN
004 IL
005 OH
006 OH
007 OH
008 IL
009 OH
010 OH
011 OH
012 OH
013 XX
014 OH
015 OH
016 OH
017 PA
018 OH
019 OH
020 IN
021 OH
022 IL
023 IN
024 OH
025 OH
026 OH
027 OH
028 OH
029 OH
030 XX
031 OH
032 NJ
033 OH
034 MA
035 MI
036 OH
037 OH
038 OH
039 KY
040 OH
041 TN
042 OH
043 IL
044 TX
045 OH
046 OH
047 OH
048 OH
049 OH
050 ME
051 OH
052 OH
053 OH
054 OH
055 NE
056 OH
057 OH
058 OH
059 OH
060 MI
061 OH
062 MD
063 OH
064 OH
065 KY
066 IL
067 OH
068 XX
069 OH
070 OH
071 OH
072 OH
073 OH
074 OH
075 OH
076 PA
077 CT
078 OH
079 OH
080 DE
081 OH
082 OH
083 IL
084 OH
085 MI
086 OH
087 MI
088 TN
089 OH
090 OH
091 MN
092 CT
093 OH
094 OH
095 MI
096 OH
097 XX
098 OH
099 OH
100 NC
101 OH
102 OH
103 CT
104 XX
105 OH
106 KY
107 OH
108 OH
109 OH
110 IL
111 IN
112 DC
113 OH
114 OH
115 OH
116 OH
117 OH
118 OH
119 UT
120 OH
121 MA
122 OK
123 OH
124 XX
125 OH
126 MD
127 IN
128 OH
129 OH
130 NJ
131 OH
132 OH
133 XX
134 IL
135 MI
136 NY
137 MI
138 OH
139 OH
140 OH
141 XX
142 OH
143 IL
144 OH
145 KY
146 VA
147 OH
148 OH
149 OH
150 OH
151 XX
152 OH
153 IL
154 MN
155 OH
156 OH
157 OH
158 OH
159 GA
160 SC
161 MN
162 OH
163 OH
164 OH
165 OH
166 PA
167 OH
168 OH
169 OH
170 OH
171 OH
172 OH
173 OH
174 OH
175 OH
176 OH
177 IL
178 OH
179 OH
180 OH
181 NC
182 OH
183 OH
184 FL
185 OH
186 OH
187 OH
188 OH
189 OH
190 OH
191 IN
192 OH
193 OH
194 OH
195 OH
196 OH
197 OH
198 OH
199 TN
200 CA
201 MI
202 OH
203 KY
204 IL
205 IN
206 OH
207 CT
208 OH
209 FL
210 OH
211 OH
212 IN
213 OH
214 OH
215 IL
216 XX
217 OH
218 OH
219 IN
220 OH
221 NY
222 PA
223 OH
224 MI
225 NY
226 MI
227 OH
228 IL
229 MO
230 PA
231 NY
232 OH
233 OH
234 OH
235 XX
236 FL
237 OH
238 OH
239 OH
240 OH
241 OH
242 XX
243 OH
244 OH
245 XX
246 NE
247 NY
248 MI
249 OH