# Stat200 week 6 homework – detailed solutions to all problems

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

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

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