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STAT 200 Week 6 Homework Problems
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9.
1.2
Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology exam 84,199 of them were female. In that same year,of the 211,693 students who took the calculus AB exam
102
,598 of them were female (“AP exam scores,” 2013). Estimate the difference in the proportion of female students taking the biology exam and female students taking the calculus AB exam using a 90% confidence level.
9.
1.5
Are there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that are mostly rural? In the state of Pennsylvania, a fairly urban state, there are 245 eight year olds diagnosed with ASD out of 18,440 eight year olds evaluated. In the state of Utah, a fairly rural state, there are 45 eight year olds diagnosed with ASD out of 2,
123
eight year olds evaluated (“Autism and developmental,” 2008). Is there enough evidence to show that the proportion of children diagnosed with ASD in Pennsylvania is more than the proportion in Utah? Test at the 1% level.
9.2
.3
All Fresh Seafood is a wholesale fish company based on the east coast of the U.S. Catalina Offshore Products is a wholesale fish company based on the west coast of the U.S. Table #9.2.5 contains prices from both companies for specific fish types (“Seafood online,” 2013)(“Buy sushi grade,” 2013). Do the data provide enough evidence to show that a west coast fish wholesaler is more expensive than an east coast wholesaler? Test at the 5% level.
Table #9.2.5: Wholesale Prices of
Fish
in Dollars
Fish
All Fresh Seafood Prices
Catalina Offshore Products Prices
Cod
19.99
17.99
Tilapi
6.00
1
3.9
9
Farmed Salmon
19.99
2
2.9
9
Organic Salmon
24.99
24.99
Grouper Fillet
29.99
19.99
Tuna
28.99
31.99
Swordfish
23.99
23.99
Sea Bass
32.99
23.99
Striped Bass
29.99
14.99
9.2.6
The British Department of Transportation studied to see if people avoid driving on Friday the
13th
. They did a traffic count on a Friday and then again on a Friday the 13th at the same two locations (“Friday the 13th,” 2013). The data for each location on the two different dates is in table #9.2.6. Estimate the mean difference in traffic count between the
6th
and the 13th using a 90% level.
Table #9.2.6: Traffic Count
Dates
6th
13th
1990, July
139246
138
548
1990, July
134
012
132908
1991, September
137055
136018
1991, September
133
732
131843
1991, December
123552
121
641
1991, December
12
113
9
118
723
1992, March
128
293
125
532
1992, March
124
631
120249
1992, November
124609
122
770
1992, November
117
584
117263
9.
3.1
The income of males in each state of the United States, including the District of Columbia and Puerto Rico, are given in table #
9.3.3
, and the income of females is given in table #
9.
3.4
(“Median income of,” 2013). Is there enough evidence to show that the mean income of males is more than of females? Test at the 1% level.
Table #9.3.3: Data of Income for Males
$42,951
$52,379
$42,544
$37,488
$49,281
$50,987
$60,705
$50,411
$66,760
$40,951
$43,902
$45,494
$41,528
$50,746
$45,183
$43,624
$43,993
$41,612
$46,313
$43,944
$56,708
$60,264
$50,053
$50,580
$40,202
$43,146
$41,635
$42,182
$41,803
$53,033
$60,568
$41,037
$50,388
$41,950
$44,660
$46,176
$41,420
$45,976
$47,956
$22,529
$48,842
$41,464
$40,285
$41,309
$43,160
$47,573
$44,057
$52,805
$53,046
$42,125
$46,214
$51,630
Table #9.3.4: Data of Income for Females
$31,862
$40,550
$36,048
$30,752
$41,817
$40,236
$47,476
$40,500
$60,332
$33,823
$35,438
$37,242
$31,238
$39,
150
$34,023
$33,745
$33,269
$32,684
$31,844
$34,599
$48,748
$46,185
$36,931
$40,416
$29,548
$33,865
$31,067
$33,424
$35,484
$41,021
$47,155
$32,316
$42,113
$33,459
$32,462
$35,746
$31,274
$36,027
$37,089
$22,117
$41,412
$31,330
$31,329
$33,184
$35,301
$32,843
$38,177
$40,969
$40,993
$29,688
$35,890
$34,381
9.3.3
A study was conducted that measured the total brain volume (TBV) (in ) of patients that had schizophrenia and patients that are considered normal. Table #9.
3.5
contains the TBV of the normal patients and table #9.
3.6
contains the TBV of schizophrenia patients (“SOCR data oct2009,” 2013). Is there enough evidence to show that the patients with schizophrenia have less TBV on average than a patient that is considered normal? Test at the 10% level.
Table #9.3.5: Total Brain Volume (in ) of Normal Patients
1663407
158
3940
129
9470
1535137
1431890
157
8698
145
3510
1650348
1288971
1366346
1326402
1503005
147
4790
1317156
1441045
1463498
1650207
152
3045
1441636
1432033
1420416
1480171
1360810
141
0213
1574808
1502702
1203344
1319737
1688990
1292641
151
2571
1635918
Table #9.3.6: Total Brain Volume (in ) of Schizophrenia Patients
1331777
1487886
106
6075
1297327
1499983
1861991
1368378
1476891
1443775
1337827
1658258
1588132
1690182
1569413
1177002
1387893
1483763
1688950
1563593
1317885
1420249
1363859
1238979
1286638
1325525
1588573
1476254
1648209
1354054
1354649
1636
119
9.3.4
A study was conducted that measured the total brain volume (TBV) (in ) of patients that had schizophrenia and patients that are considered normal. Table #9.3.5 contains the TBV of the normal patients and table #9.3.6 contains the TBV of schizophrenia patients (“SOCR data oct2009,” 2013). Compute a 90% confidence interval for the difference in TBV of normal patients and patients with Schizophrenia.
9.
3.8
The number of cell phones per
100
residents in countries in Europe is given in table #9.3.9 for the year 2010. The number of cell phones per 100 residents in countries of the Americas is given in table #9.3.10 also for the year 2010 (“Population reference bureau,” 2013). Find the 98% confidence interval for the different in mean number of cell phones per 100 residents in Europe and the Americas.
Table #9.3.9: Number of Cell Phones per 100 Residents in Europe
100
76
100
130
75
84
112
84
138
133
118
134
126
188
129
93
64
128
124
122
109
121
127
152
96
63
99
95
151
147
123
95
67
67
118
125
110
115
140
115
141
77
98
102
102
112
118
118
54
23
121
126
47
Table #9.3.10: Number of Cell Phones per 100 Residents in the Americas
158
117
106
159
53
50
78
66
88
92
42
3
150
72
86
113
50
58
70
109
37
32
85
101
75
69
55
115
95
73
86
157
100
119
81
113
87
105
96
11.
3.2
Levi-Strauss Co manufactures clothing. The quality control department measures weekly values of different suppliers for the percentage difference of waste between the layout on the computer and the actual waste when the clothing is made (called run-up). The data is in table #
1
1.3
.3, and there are some negative values because sometimes the supplier is able to layout the pattern better than the computer (“Waste run up,” 2013). Do the data show that there is a difference between some of the suppliers? Test at the 1% level.
Table #11.3.3: Run-ups for Different Plants Making Levi Strauss Clothing
Plant 1
Plant 2
Plant 3
Plant 4
Plant 5
1.2
16.4
12.1
11.5
24
10.1
-6
9.7
10.2
-3.7
-2
-11.6
7.4
3.8
8.2
1.5
-1.3
-2.1
8.3
9.2
-3
4
10.1
6.6
-9.3
–
0.7
17
4.7
10.2
8
3.2
3.8
4.6
8.8
15.8
2.7
4.3
3.9
2.7
22.3
-3.2
10.4
3.6
5.1
3.1
-1.7
4.2
9.6
11.2
1
6.8
2.4
8.5
9.8
5.9
11.3
0.3
6.3
6.5
13
12.3
3.5
9
5.7
6.8
16.9
-0.8
7.1
5.1
14.5
19.4
4.3
3.4
5.2
2.8
19.7
-0.8
7.3
13
3
-3.9
7.1
42.7
7.6
0.9
3.4
1.4
70.2
1.5
0.7
3
8.5
2.4
6
1.3
2.9
11.3.4
A study was undertaken to see how accurate food labeling for calories on food that is considered reduced calorie. The group measured the amount of calories for each item of food and then found the percent difference between measured and labeled food, . The group also looked at food that was nationally advertised, regionally distributed, or locally prepared. The data is in table #11.3.5 (“Calories datafile,” 2013). Do the data indicate that at least two of the mean percent differences between the three groups are different? Test at the 10% level.
Table #11.3.5: Percent Differences Between Measured and Labeled Food
National Advertised
Regionally Distributed
Locally Prepared
2
41
15
-28
46
60
-6
2
250
8
25
145
6
39
6
-1
16.5
80
10
17
95
13
28
3
15
-3
-4
14
-4
34
-18
42
10
5
3
-7
3
-0.5
-10
6
STAT 200 Week 6 Homework Problems
9.1.2
Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology exam 84,199 of them were female. In that same year,of the 211,693 students who took the calculus AB exam 102,598 of them were female (“AP exam scores,” 2013). Estimate the difference in the proportion of female students taking the biology exam and female students taking the calculus AB exam using a 90% confidence level.
9.1.5
Are there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that are mostly rural? In the state of Pennsylvania, a fairly urban state, there are 245 eight year olds diagnosed with ASD out of 18,440 eight year olds evaluated. In the state of Utah, a fairly rural state, there are 45 eight year olds diagnosed with ASD out of 2,123 eight year olds evaluated (“Autism and developmental,” 2008). Is there enough evidence to show that the proportion of children diagnosed with ASD in Pennsylvania is more than the proportion in Utah? Test at the 1% level.
9.2.3
All Fresh Seafood is a wholesale fish company based on the east coast of the U.S. Catalina Offshore Products is a wholesale fish company based on the west coast of the U.S. Table #9.2.5 contains prices from both companies for specific fish types (“Seafood online,” 2013)(“Buy sushi grade,” 2013). Do the data provide enough evidence to show that a west coast fish wholesaler is more expensive than an east coast wholesaler? Test at the 5% level.
Table #9.2.5: Wholesale Prices of Fish in Dollars
Fish
All Fresh Seafood Prices
Catalina Offshore Products Prices
Cod
19.99
17.99
Tilapi
6.00
13.99
Farmed Salmon
19.99
22.99
Organic Salmon
24.99
24.99
Grouper Fillet
29.99
19.99
Tuna
28.99
31.99
Swordfish
23.99
23.99
Sea Bass
32.99
23.99
Striped Bass
29.99
14.99
9.2.6
The British Department of Transportation studied to see if people avoid driving on Friday the 13th. They did a traffic count on a Friday and then again on a Friday the 13th at the same two locations (“Friday the 13th,” 2013). The data for each location on the two different dates is in table #9.2.6. Estimate the mean difference in traffic count between the 6th and the 13th using a 90% level.
Table #9.2.6: Traffic Count
Dates
6th
13th
1990, July
139246
138548
1990, July
134012
132908
1991, September
137055
136018
1991, September
133732
131843
1991, December
123552
121641
1991, December
121139
118723
1992, March
128293
125532
1992, March
124631
120249
1992, November
124609
122770
1992, November
117584
117263
9.3.1
The income of males in each state of the United States, including the District of Columbia and Puerto Rico, are given in table #9.3.3, and the income of females is given in table #9.3.4 (“Median income of,” 2013). Is there enough evidence to show that the mean income of males is more than of females? Test at the 1% level.
Table #9.3.3: Data of Income for Males
$42,951
$52,379
$42,544
$37,488
$49,281
$50,987
$60,705
$50,411
$66,760
$40,951
$43,902
$45,494
$41,528
$50,746
$45,183
$43,624
$43,993
$41,612
$46,313
$43,944
$56,708
$60,264
$50,053
$50,580
$40,202
$43,146
$41,635
$42,182
$41,803
$53,033
$60,568
$41,037
$50,388
$41,950
$44,660
$46,176
$41,420
$45,976
$47,956
$22,529
$48,842
$41,464
$40,285
$41,309
$43,160
$47,573
$44,057
$52,805
$53,046
$42,125
$46,214
$51,630
Table #9.3.4: Data of Income for Females
$31,862
$40,550
$36,048
$30,752
$41,817
$40,236
$47,476
$40,500
$60,332
$33,823
$35,438
$37,242
$31,238
$39,150
$34,023
$33,745
$33,269
$32,684
$31,844
$34,599
$48,748
$46,185
$36,931
$40,416
$29,548
$33,865
$31,067
$33,424
$35,484
$41,021
$47,155
$32,316
$42,113
$33,459
$32,462
$35,746
$31,274
$36,027
$37,089
$22,117
$41,412
$31,330
$31,329
$33,184
$35,301
$32,843
$38,177
$40,969
$40,993
$29,688
$35,890
$34,381
9.3.3
A study was conducted that measured the total brain volume (TBV) (in ) of patients that had schizophrenia and patients that are considered normal. Table #9.3.5 contains the TBV of the normal patients and table #9.3.6 contains the TBV of schizophrenia patients (“SOCR data oct2009,” 2013). Is there enough evidence to show that the patients with schizophrenia have less TBV on average than a patient that is considered normal? Test at the 10% level.
Table #9.3.5: Total Brain Volume (in ) of Normal Patients
1663407
1583940
1299470
1535137
1431890
1578698
1453510
1650348
1288971
1366346
1326402
1503005
1474790
1317156
1441045
1463498
1650207
1523045
1441636
1432033
1420416
1480171
1360810
1410213
1574808
1502702
1203344
1319737
1688990
1292641
1512571
1635918
Table #9.3.6: Total Brain Volume (in ) of Schizophrenia Patients
1331777
1487886
1066075
1297327
1499983
1861991
1368378
1476891
1443775
1337827
1658258
1588132
1690182
1569413
1177002
1387893
1483763
1688950
1563593
1317885
1420249
1363859
1238979
1286638
1325525
1588573
1476254
1648209
1354054
1354649
1636119
9.3.4
A study was conducted that measured the total brain volume (TBV) (in ) of patients that had schizophrenia and patients that are considered normal. Table #9.3.5 contains the TBV of the normal patients and table #9.3.6 contains the TBV of schizophrenia patients (“SOCR data oct2009,” 2013). Compute a 90% confidence interval for the difference in TBV of normal patients and patients with Schizophrenia.
9.3.8
The number of cell phones per 100 residents in countries in Europe is given in table #9.3.9 for the year 2010. The number of cell phones per 100 residents in countries of the Americas is given in table #9.3.10 also for the year 2010 (“Population reference bureau,” 2013). Find the 98% confidence interval for the different in mean number of cell phones per 100 residents in Europe and the Americas.
Table #9.3.9: Number of Cell Phones per 100 Residents in Europe
100
76
100
130
75
84
112
84
138
133
118
134
126
188
129
93
64
128
124
122
109
121
127
152
96
63
99
95
151
147
123
95
67
67
118
125
110
115
140
115
141
77
98
102
102
112
118
118
54
23
121
126
47
Table #9.3.10: Number of Cell Phones per 100 Residents in the Americas
158
117
106
159
53
50
78
66
88
92
42
3
150
72
86
113
50
58
70
109
37
32
85
101
75
69
55
115
95
73
86
157
100
119
81
113
87
105
96
11.3.2
Levi-Strauss Co manufactures clothing. The quality control department measures weekly values of different suppliers for the percentage difference of waste between the layout on the computer and the actual waste when the clothing is made (called run-up). The data is in table #11.3.3, and there are some negative values because sometimes the supplier is able to layout the pattern better than the computer (“Waste run up,” 2013). Do the data show that there is a difference between some of the suppliers? Test at the 1% level.
Table #11.3.3: Run-ups for Different Plants Making Levi Strauss Clothing
Plant 1
Plant 2
Plant 3
Plant 4
Plant 5
1.2
16.4
12.1
11.5
24
10.1
-6
9.7
10.2
-3.7
-2
-11.6
7.4
3.8
8.2
1.5
-1.3
-2.1
8.3
9.2
-3
4
10.1
6.6
-9.3
-0.7
17
4.7
10.2
8
3.2
3.8
4.6
8.8
15.8
2.7
4.3
3.9
2.7
22.3
-3.2
10.4
3.6
5.1
3.1
-1.7
4.2
9.6
11.2
16.8
2.4
8.5
9.8
5.9
11.3
0.3
6.3
6.5
13
12.3
3.5
9
5.7
6.8
16.9
-0.8
7.1
5.1
14.5
19.4
4.3
3.4
5.2
2.8
19.7
-0.8
7.3
13
3
-3.9
7.1
42.7
7.6
0.9
3.4
1.4
70.2
1.5
0.7
3
8.5
2.4
6
1.3
2.9
11.3.4
A study was undertaken to see how accurate food labeling for calories on food that is considered reduced calorie. The group measured the amount of calories for each item of food and then found the percent difference between measured and labeled food, . The group also looked at food that was nationally advertised, regionally distributed, or locally prepared. The data is in table #11.3.5 (“Calories datafile,” 2013). Do the data indicate that at least two of the mean percent differences between the three groups are different? Test at the 10% level.
Table #11.3.5: Percent Differences Between Measured and Labeled Food
National Advertised
Regionally Distributed
Locally Prepared
2
41
15
-28
46
60
-6
2
250
8
25
145
6
39
6
-1
16.5
80
10
17
95
13
28
3
15
-3
-4
14
-4
34
-18
42
10
5
3
-7
3
-0.5
-10
6
measured− labeled( )
labeled
*100%
measured-labeled
( )
labeled
*100%
mm3
mm
3
