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