MATH 205 WU The Adirondack Mountains Acid Rain & pH Measurement Lab Report

Description

Do the statistics class homework using R Commander. I have included the data excel needed to do the questions. Import the appropriate sheet in R Commander for each question. Do question one(a to f) with ”Streams” sheet. Do question two with the ”Braking” sheet. Do question three with ”Traffic Stops” sheet. Do question four with ”Cholesterol” sheet.

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MATH 205
Homewor
1. Researchers collected samples of water from streams in the Adirondack Mountains to
investigate the effects of acid rain. They measured the pH (acidity) of the water and
classified the streams with respect to the kind of substrate (type of rocks over which they
flow). A lower pH means the water is more acidic. Are there differences in terms of
acidity between the different types of substrate (limestone, mixed, and shale)?
a. Screenshot of numerical summaries by substrate
b. Screenshot of boxplots by substrate
c. Null and alternative hypotheses
d. Appropriate test results
e. Check assumptions
i. Each group is normally distributed
ii. Ratio of lowest SD and highest SD
iii. Independence
f. Conclusion( make two conclusions. The first conclusion should be the statistical
conclusion and the second conclusion should be an explanation of the statistical
conclusion to people with no statistical background knowledge)
2. A tire manufacturer tested the braking performance of one of its tire models on a test
track. The company tried the tires on 10 different cars, recording the stopping distance for
each car on both wet and dry pavement. Is there a difference between dry and wet
pavements for this type of tire in terms of braking performance?
a. Null and alternative hypotheses
b. Histogram of differences between wet and dry pavement
c. Appropriate test result
d. Conclusion( make two conclusions. The first conclusion should be the statistical
conclusion and the second conclusion should be an explanation of the statistical
conclusion to people with no statistical background knowledge)
3. Many states and localities now collect data on traffic stops regarding the race of the
driver. The initial concern was that Black drivers were being stopped more often. With
more data in hand, attention has turned to other issues. For example, data from 2533
traffic stops in Cincinnati report the race of the driver (Black, White, or Other) and
whether the traffic stop resulted in a search of the vehicle. Is there evidence that race is a
factor in vehicle searches?
Black
Not Searched
White
787
Other
594
Total
27
1408
Searched
Total
a.
b.
c.
d.
e.
f.
813
1600
293
887
19
46
1125
2533
Explanatory variable and type
Response variable and type
Null and alternative hypotheses
Bar chart of proportions (use Excel)
Appropriate test result
Conclusion( make two conclusions. The first conclusion should be the statistical
conclusion and the second conclusion should be an explanation of the statistical
conclusion to people with no statistical background knowledge)
4. Does a person’s cholesterol level tend to change with age? This dataset was collected
from 1406 adults aged 45 to 62.
a. Explanatory variable and type
b. Response variable and type
c. Screenshot of scatterplot + regression line
d. Correlation coefficient
e. Regression model
f. Check assumptions
i. Linear
ii. Constant variation
iii. Normality of residuals
iv. Independence
g. Conclusion( make two conclusions. The first conclusion should be the statistical
conclusion and the second conclusion should be an explanation of the statistical
conclusion to people with no statistical background knowledge)
Stream
BEAR
FISH
FOX
GRUNLEY
ABIJAH
SSANDY
DENNING
GULF
RAYSTONE
DEER
EDICK
LUTHER
BEARGULF
NONAME
NOBRANCH
SANDYLIB
SANDYSPR
SKINNER
LINDSAY
RAYSTONE
SSANDY
STEBBINS
STONY
MILL
SWICKS
LSTONEY
GREEN
KELSEY
COLDCREE
MILLRUT
SKINNERM
STAPLIN
STONEYHE
DEERLICK
SANDYBEL
BEAR
SOUTHWKS
STONYKEL
MILL
CEMETARY
SUBSTRATE PH
S
S
S
S
S
S
S
S
S
S
S
S
S
S
M
M
M
M
M
M
M
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
TEMP
7
7
6,75
7,2
6,75
6,8
7
7,2
7
6,5
6,8
6,8
7
6,8
7,5
7,5
7,8
7,5
7
7,25
7,25
7,5
7,5
7,75
8
7,75
7,75
8
8
8
7
8
8
8
8
7,5
7,75
8
7,75
7,5
BCI
2
2
9
9
8
10
11
9
9
5
4
4
5
5
7
2
5
4
6
9
9
2
6
9
10
9
8
8
9
7
6
6
10
11
9
9
5
1,5
1,5
7
HARD
1389,24
1336
1417,27
1264,47
1412,81
1483,84
1367,07
1307,88
1503,25
1332,21
1304,76
1349,22
1419,93
1605,11
1114,83
1192,93
1578,67
1336,13
1467,96
1485,15
1447,51
1026,57
1292,46
1228,84
1108,9
1141,71
1384,46
649,36
1247,4
1264,35
1337,91
1095,78
1091,5
1105,97
1439,15
1365,07
1156,63
1379,59
1298,5
1154,99
51,3
68,4
68,4
51,3
34,2
51,3
51,3
51,3
51,3
34,2
34,2
51,3
34,2
34,2
188,1
119,7
119,7
34,2
34,2
34,7
51,3
171
171
188,1
256,5
171
188,1
205,2
239,4
153,9
34,2
188,1
188,1
171
136,8
68,4
495,9
513
461,7
495,9
STONYGRE
STONY
LSTONY
JACOBS
STAPLINB
KELSEYC
FELTSMIL
STEBBINS
KELSEYBR
STAPLING
COLD
LSANDY
SANDY
SKINNER
SKINNERE
SKINNR11
SANDYSPR
SANDY
LUTHER
EDICK
BARNSCOR
RAYSTONL
FISHBRN
DEER
BEARLORR
ABIJAH
FISH171
FOX
SANDYWHI
PLEASANT
FELTS MILLS
STAPLIN(R26)
STAPLIN(TRB)
JACOBS
COLD
KELSEY(CAY)
MILL(RT81)
MILL(S.SPG)
COLLEEN(SHB)
GREEN
L
L
L
L
L
L
L
L
L
L
L
M
M
M
M
M
M
S
S
S
S
S
S
S
S
S
S
S
S
S
L
L
L
L
L
L
L
L
L
L
L
7,85
7,7
7,9
7,3
7,6
8,1
7,8
7,3
7,5
8
8
7
7
7,5
7,15
7,15
7,5
7
7
6,5
7
6,8
7,3
7
7
7
6,8
6,8
6,8
7,5
7,5
7,5
8
7,5
8
8
7,5
8
8
8
7,5
5
7
7
2
4
5
5
1
10
8
9
0
0
2
2
2
8
0
3
0
2
4
1
0
2
2
3
4
3
8
6
7
7
6
5
9
7
6
6
0
3
1420,79
1094,25
980,43
1260,41
1282,22
831,79
1136,8
834,14
801,84
1296,71
1125,06
1285,06
1316,91
1395,15
1403,2
1391,31
987,2
1391,34
1375,41
1276,94
1356,52
*
1426,91
1386,82
*
*
*
1520,5
1438,82
1255,29
1207,93
1273,51
1142,31
1000,64
1156,12
1195,51
875,09
1266,53
*
1322,35
1160,4
478,8
410,4
342
171
188,1
222,3
188,1
171
444,6
444,6
513
102,6
68,4
136,8
102,6
68,4
136,8
68,4
34,7
34,2
34,2
34,2
51,3
34,2
34,2
34,2
34,2
34,2
34,2
256,5
222,3
273,6
222,3
205,2
256,5
307,8
256,5
273,6
256,5
222,3
307,8
S.SANDY(ELL)
BEAR(WOF81)
N.BRANCH(VA)
LSANDY(FISH)
SKINNER(GCS)
COLLEEN(DEN)
SKINNER(VEL)
SKINNER(VW)
LSANDY(CHUR)
LSANDY(VANA)
LINDSAY(NCH)
FRENCHSETTLE
RAYST(REDF)
FOX(LRDF)
ABIJAH178
ABIJAHBULL
ABIJAHNICHOL
RAYST(R11)
S.SANDY(7×9)
EDICK
FISH(LOWE)
FISH(WPARK)
LINDSAYS.BRA
MILL
KELSEY
COLD
STAPLIN
JACOBS
CEMETERY
STONY
FELTS MILLS
LITTLE SANDY
SKINNER
FISH
GULF
RAYSTONE(PPM)
FOX
RAYSTONE(RED)
JOEL CAMP
BIG BROOK
ABIJAH
L
L
L
L
L
L
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
L
L
L
L
L
L
L
L
M
M
M
M
S
S
S
S
S
S
7,5
7,4
7,5
7
7
7,5
7
7
7
7
7
6,8
6,5
7
7
7
7
7
6,7
6,5
7,2
7,5
7,5
8
7,5
7,9
8
8
7,5
7,5
8,2
7
7
7,5
7
7
7
7
7
6,9
7
0
0
0
0
0
0
0
0
0
0
0
2
5
3
2
2
3
0
2
2
5
4
1
4
3
8
4
3
2
4
4
4
3
1
5
1
1,5
2
1
0
1
1435,72
1229,1
1402,73
1469,29
1325,68
1354,45
1423,33
1433,4
1501,44
1387,59
1413,89
1440,74
1453,97
1508,42
1382,3
1491,86
1462,38
1510,32
1343,74
1356,9
1431,82
1504,65
1301,78
1237
834
1189
1269
1241
1193
1192
1309
1335
1343
1382
1473
1395
1384
1344
1264
1318
1366
102,6
36,8
239,4
102,6
119,7
188,1
85,5
102,6
102,6
102,6
102,6
68,4
102,6
85,5
85,5
68,4
85,5
102,6
102,6
136,8
102,6
136,8
171
239,4
239,4
119,7
256,5
256,5
222,3
222,3
205,2
85,5
68,4
102,6
68,4
68,4
68,4
51,3
85,5
51,3
51,3
DENING
DEER
LUTHER
RAYSTONE(DIAM)
KELSEY
KELSEY
CHAUMO
CHAUMO
MILL
MILL
SANDY
SANDY
BIG B
BIG B
LITTLE S
LITTLE S
BEAR
BEAR
SKINNER
SKINNER
COLD
COLD
FELTS M
FELTS M
STONY
STONY
SKINNER
BEAR
SKINNER
SKINNER
BEAR-MP
SKINNER
MILL
STONY
SANDY LIBERTY
GREEN/STONY
LITTLE STONY
MILL CREEK
STEBBINS
SHINGLE GULF
TRIB SANDY, OSTRICH
S
S
S
S
L
L
L
L
L
L
M
L
S
S
S
M
S
M
M
M
L
L
L
L
L
L
M
S
M
S
M
M
L
L
L
L
L
L
S
S
S
7
7
7
6,7
7,4
7,6
6,4
6,8
7,9
7,7
7,7
7,3
7
7
7
7
7,2
7
7
7,5
7,8
7,7
7,8
7,7
7,7
7,7
7,2
7
7
6,8
7,3
7,1
8
8
7,5
7,75
7,75
7,5
7
6,5
7
2
3
3
8
2
3
2
5
1
1
3
4
1
1
3
3,5
0
1
4
2
9
5
3
4
4
6
2
2
2,5
2
2
2
4
4
4
4
4
4
2
2
2
1300
1291
1205
1326
*
*
*
*
1149,57
1094,52
1536,38
1209,9
1406,4
1385,05
1399,01
1461,79
1289,32
1301,42
1397,65
1359,64
1142,44
1099,69
1100,31
984,38
1295,79
1097,81
1326
1345,42
1332,8
1363,49
1330,54
1341,77
1192,5
1096,97
1127,22
1271,5
1010,92
1208,93
1146,92
1381,07
1473,48
68,4
34,2
34,2
34,2
205,2
205,2
85,5
68,4
188,1
171
171
171
68,4
102,6
51,3
51,3
51,3
51,3
119,7
102,6
239,4
205,2
188,1
171
205,2
171
85,5
68,4
85,5
68,4
68,4
68,4
205,2
222,3
136,8
222,3
205,2
222,3
68,4
51,3
68,4
FISH CREEK BROWNS
TRIB SANDY PAT RD
OILY CREEK
PLEASANT
LITTLE DEER LICK
LITTLE SANDY
TROUT BROOK
FOX CREEK
COTTEL CREEK
S
S
L
L
L
S
S
S
S
7
7,1
7,5
7,6
7,6
6,8
7,2
6,8
6,5
2
2
2
4
3
2
2
2
1
1368,98
1218,48
963,14
1126,54
1021,08
1294,55
1380,32
1298,57
1370,31
68,4
102,6
190
171
136,8
51,3
68,4
68,4
68,4
ALK
PHOS
0
17,1
51,3
51,3
34,2
51,3
68,4
51,3
51,3
34,2
34,2
34,2
51,3
34,2
102,6
188,1
119,7
34,2
34,2
51,3
51,3
188,1
102,6
102,6
205,2
171
85,5
171
222,3
0
51,3
171
188,1
136,8
119,7
85,5
188
188
205
188
0,05
0,07
0,04
0,11
0,12
0,06
0,06
0,05
0,26
0,16
0,05
0,1
0,07
0,05
0,06
0,29
0,1
0
0
0
0,01
0,51
0,01
0,01
0,01
0,03
0,09
0,08
0,28
0,12
0,05
0,15
0,04
0,06
0,03
0,05
0,18
0,13
0,13
0,18
188
205
137
153,9
171
171
153,9
153,9
171
188,1
205,2
51
34
68
51
34
102,6
34
51,3
51,3
51,3
51,3
51,3
51,3
51,3
68,4
51,3
51,3
34,2
85,5
119,7
153,9
188,1
68,4
136,8
205,2
188,1
153,9
171
153,9
171
0,07
0,13
0,29
0,08
0,2
0,06
0,11
0,51
0,16
0,15
0,14
0,12
0,08
0,07
0,18
0,11
0,22
0,03
0,15
0,13
0,1
0,27
0,08
0,2
0,3
0,32
0,32
0,06
0,15
0,15
0,08
0,03
0,2
0,01
0,13
0,07
0,84
0,25
0,09
0,01
0,02
68,4
34,2
171
51,3
68,9
153,9
51,3
51,3
34,2
51,3
51,3
51,3
51,3
51,3
51,3
51,3
51,3
51,3
51,3
51,3
51,3
85,5
102,6
205,2
188,1
239,4
205,2
188,1
205,2
188,1
188,1
68,4
51,3
85,5
68,4
68,4
68,4
51,3
68,4
51,3
51,3
0,02
0,17
0,01
0,06
0,45
0,32
0,05
0,03
0,25
0,06
0,08
0,08
0,15
0,09
0,07
0,05
0,06
0
0,06
0,11
0,08
0,06
0,08
0,09
0,09
3,78
0,22
0,08
0,09
0,18
0,33
0,12
0,11
0,04
0,01
0,34
0,12
0,51
0,23
0,33
0,2
68,4
68,4
68,4
51,3
171
9
51,3
68,4
153,9
136,8
119,7
119,7
34,2
51,3
34,2
34,2
51,3
51,3
34,2
51,3
205,2
205,2
171
171
171
171
51,3
51,3
51,3
51,3
51,3
51,3
171
153,9
119,7
188,1
171
188,1
51,3
51,3
68,4
0,93
0,15
0,04
0,2
0,38
0,26
0,49
1,03
0,24
0,25
0,2
0,2
3,8
0,46
0,25
0,01
0,83
0,21
0,02
0,05
0,11
0,21
0,05
0,1
0,17
0,08
0,06
0,01
0,1
0,01
0,01
0,01
0,05
0,05
0,01
0,01
0,01
0,06
0,01
0,09
0,04
51,3
68,4
153,9
136,8
136,8
34,2
68,4
51,3
51,3
0,01
0,25
0,38
0,18
0,02
0,01
0,01
0,01
0,01
Vehicle
Dry
1
2
3
4
5
6
7
8
9
10
Wet
145
152
141
143
131
148
126
140
135
133
211
191
220
207
198
208
206
177
183
223
Black
Not Searched
Searched
Total
White
787
813
1600
Other
594
293
887
Total
27
19
46
1408
1125
2533
Age
Chol
45
49
47
48
49
47
48
48
46
45
45
47
49
45
46
45
45
46
48
46
45
48
45
46
45
48
48
46
48
46
47
48
47
45
49
45
48
47
45
49
216
237
215
340
149
165
196
229
204
183
183
182
218
162
195
194
256
192
173
205
217
232
140
270
237
243
223
246
242
195
185
200
224
200
184
200
180
284
199
201
48
48
48
45
45
46
46
46
46
46
47
46
46
45
48
45
48
49
47
45
46
45
49
49
48
49
45
47
46
46
48
47
46
46
49
46
45
47
46
49
46
258
240
200
302
225
210
194
250
192
230
243
280
258
250
212
225
248
221
225
216
275
280
172
209
195
142
227
243
227
227
198
183
247
255
230
270
256
255
231
276
225
45
47
48
49
48
47
47
49
45
48
45
48
47
47
49
46
46
47
45
45
47
46
46
45
47
46
46
48
47
46
47
49
48
46
45
48
47
49
45
47
46
204
215
149
232
232
288
240
183
198
250
198
220
243
250
237
174
180
224
237
263
225
238
278
249
198
187
198
213
238
165
255
188
194
276
248
232
244
263
220
216
191
47
46
45
47
45
47
47
46
46
49
49
45
48
47
45
48
45
48
49
49
45
48
45
47
49
47
49
46
45
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Name: Tsion Yimenu
MATH 205
Final Exam
1. Researchers collected samples of water from streams in the Adirondack Mountains to
investigate the effects of acid rain. They measured the pH (acidity) of the water and
classified the streams with respect to the kind of substrate (type of rocks over which they
flow). A lower pH means the water is more acidic. Are there differences in terms of
acidity between the different types of substrate (limestone, mixed, and shale)?
a. Screenshot of numerical summaries by substrate
b. Screenshot of boxplots by substrate
c. Null and alternative hypotheses
𝐻0 : 𝜇1 = 𝜇2 = 𝜇3
𝐻𝑎 : 𝐴𝑡 𝑙𝑒𝑎𝑠𝑡 𝑡𝑤𝑜 𝑜𝑟 𝑚𝑜𝑟𝑒 𝑚𝑒𝑎𝑛𝑠 𝑎𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡
d. Appropriate test results
e. Check assumptions
i. Each group is normally distributed
Limestone group is approximately normal distributed. Mixed group is slightly right-skewed and
finally shale group is left-skewed. Thus, this conclusion is not fully met.
ii. Ratio of lowest SD and highest SD
0.3241
= 1.5067
0.2151
Because the ratio is less than 2, we conclude that the assumption of equal population variances is
satisfied.
iii. Independence
We have an independent simple random sample.
f. Conclusion
Because the p-value is small (i.e., less than 0.05) we reject the null hypothesis. There is enough
evidence to support the claim that the mean pH is not the same for al substrate. In other words,
there are differences in terms of acidity between the different types of substrate.
2. A tire manufacturer tested the braking performance of one of its tire models on a test
track. The company tried the tires on 10 different cars, recording the stopping distance for
each car on both wet and dry pavement. Is there a difference between dry and wet
pavements for this type of tire in terms of braking performance?
a. Null and alternative hypotheses
𝐻0 : 𝜇𝑑 = 0
𝐻𝑎 : 𝜇𝑑 ≠ 0
b. Histogram of differences between wet and dry pavement
c. Appropriate test result
d. Conclusion
Because the p-value is small (i.e., less than 0.05) we reject the null hypothesis. There
is enough evidence to support the claim that there is a difference between dry and wet
pavements for this type of tire in terms of braking performance.
3. Many states and localities now collect data on traffic stops regarding the race of the
driver. The initial concern was that Black drivers were being stopped more often. With
more data in hand, attention has turned to other issues. For example, data from 2533
traffic stops in Cincinnati report the race of the driver (Black, White, or Other) and
whether the traffic stop resulted in a search of the vehicle. Is there evidence that race is a
factor in vehicle searches?
Black
Not Searched
Searched
Total
White
787
813
1600
Other
594
293
887
a. Explanatory variable and type
Race, Qualitative.
b. Response variable and type
Vehicle searches, Qualitative.
c. Null and alternative hypotheses
𝐻0 : 𝑅𝑎𝑐𝑒 𝑎𝑛𝑑 𝑣𝑒ℎ𝑖𝑐𝑙𝑒 𝑠𝑒𝑎𝑟𝑐ℎ𝑒𝑠 𝑎𝑟𝑒 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡
𝐻𝑎 : 𝑅𝑎𝑐𝑒 𝑎𝑛𝑑 𝑣𝑒ℎ𝑖𝑐𝑙𝑒 𝑠𝑒𝑎𝑟𝑐ℎ𝑒𝑠 𝑎𝑟𝑒 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡
d. Bar chart of proportions (use Excel)
Total
27
19
46
1408
1125
2533
Bar graph
0.8000
0.7000
0.6000
0.5000
0.4000
0.3000
0.2000
0.1000
0.0000
Not Searched
Searched
Black
White
Other
e. Appropriate test result
f. Conclusion
Because the p-value is small (i.e., less than 0.05) we reject the null hypothesis. There
is enough evidence to support the claim that race and vehicle searches are dependent.
In other words, race is a factor in vehicle searches.
4. Does a person’s cholesterol level tend to change with age? This dataset was collected
from 1406 adults aged 45 to 62.
a. Explanatory variable and type
Age, Quantitative
b. Response variable and type
Cholesterol level, Quantitative.
c. Screenshot of scatterplot + regression line
d. Correlation coefficient
0.0798
e. Regression model
𝑐ℎ𝑜𝑙𝑒𝑠𝑡𝑒𝑟𝑜𝑙 = 0.7716 ∗ 𝐴𝑔𝑒 + 194.2325
f. Check assumptions
i. Linear
The residual plot does not exhibit any obvious pattern. Thus, this assumption is met.
ii. Constant variation
The vertical spread of the points in the residual plot are roughly the same across the plot. Thus,
this assumption is met.
iii. Normality of residuals
From the normal QQ plot we can check the normality assumption. Because most of the points fit
into the straight line we can say that this assumption is met.
iv. Independence
We have independent simple random samples.
g. Conclusion
Because the p-value is small (i.e., less than 0.05). There is enough evidence to support the claim
that there is a linear relationship between Age and Cholesterol level. In other words, Cholesterol
level tends to change with Age; even the older a person gets, the bigger will be his cholesterol
level.

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alternative hypotheses

Null hypotheses

acid rain

boxplots

the Adirondack Mountains

pH Measurement

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