Many high school students take 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.
Answer:
n2= 211693 P2=102598/211693= 0.4847
n1= 144796 P1= 84199/144796 = 0.5815
Confidence level at 90%;
(0.4847(1-0.4847)/211693 (0.5815-0.4847) +1.645√ (0.5815(1-0.5815)/144796) = 0.0996
(0.4847(1-0.4847)/211693) (0.5815-0.4847)-1.645√ (0.5815(1-0.5815)/144796) = 0.0941
Therefore, the confidence level range is (0.0941, 0.0996)
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.
Delegate your assignment to our experts and they will do the rest.
Answer:
P2= 45/2123= 0.0212
P1= 245/18440= 0.0133
At a significance level of 1%
P= (45+245) / (2123+18440) = 0.0141
SE= √ ((0.0141(1-0.0141) (1/2123)) + ((1/18440) = 0.0027
Z= ((245/18440) – (45/2123)) / 0.0027 = -2.9297
The claim stating that the percentage of children who have been identified with ASD in Utah is less than the proportion in Pennsylvania.
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 |
| Tilapia |
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 |
Answer:
y=194.91/9 = 21.66 S2= 250.00/8= 31.25
X= 216.92/9=24.10 S1=534.53/8= 66.82
Test Statistic: t= 2.45/ (7.39/√9) = 0.995
T= (24.10-21.66)/√ (31.25/8)) = ((66.82/8) 2.44/2.11 = 1.16
The P value is 0.85. The P value is found to be less than the test statistics, t
This justifies that East Coast is cheaper than West Coast wholesaler
9.2.6
The British Department of Transportation studied to see if people avoid driving on Friday the 13 th . They did a traffic count on a Friday and then again on a Friday the 13 th at the same two locations ("Friday the 13th," 2013) . The data for each location on the two different dates are in table #9.2.6. Estimate the mean difference in traffic count between the 6 th and the 13 th 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 |
Answer:
E= 681.7
D = 1835.8
Upper bound=681.7+1835.8=2517.5
Lower bound=1835.8-681.7= 1154.1
The difference in the means of traffic count that lies between 6 th and 13 th at a confidence level of 90% lies between 1154.1 and 2517.5.
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 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 |
Answer:
Test Statistic t, = 9935/1294.02= 7.68
At 1% probability level: 2.364 in this P value is less than the test statistics
This justifies that the mean income of the females is less than that of the males
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 |
Answer:
P value: 0.37 is greater than α: 0.10
From these values, there is lack of sufficient evidence to show that on an average, patients suffering from schizophrenia have less TBV
At C.I of 90%; 18207+/-52176= (-33969, 70383) is the difference existing in TBV of patients who are normal and Schizophrenic patients
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.
Answer:
At 90%: 18207+/-52176= Difference in TBV of normal patients and Schizophrenic patients is (-33969, 70383).
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 difference in a 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 |
Answer:
C1=2.326√ (29.965 2 /53) + (35.155 2 /39)) + (108.151-87.205) = 37.1664
2.326√ (29.965 2 /53) + (35.155 2 /39)) + (108.151-87.205) = 4.7252
At C.I of 98 %( 4.7252, 37.1664) is the mean difference between the cell phone numbers per 100 residents in America and Europe
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.
Answer:
P value: 0.334 is greater than α at 0.01
There lacks sufficient evidence that shows that there exists a difference among the suppliers
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 labelling for calories on food that is considered reduced calorie. The group measured the number of calories for each item of food and then found the per cent difference between measured and labelled 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 per cent differences between the three groups are different? Test at the 10% level.
Answer:
P value: 0.0001 is less than α: 0.10
The claim can be supported by the evidence available that there are different for at least two of the mean per cent differences between the three groups
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 |
