Final Exam Statistics 300: Introduction to Probability and Statistics Fall Semester 2011 Cosumnes College Instructor: L.C. Larsen Instructions Time: 2 hours and 5 minutes on 12/9,12/12, or 12/13. Materials: Open book, notes, homework, etc. Instruments: Calculator/Laptop of student's choice No phones or consultants Except to call the instructor : 346-6324. Answers to confidence interval problems must include the expression (the formula) in symbolic form and the expression with all of the values inserted in the proper places. Then, the final answer can be calculated by any method or device. Unless a p-value is given in the problem, each hypothesis test problem must include all four parts of the traditional approach to hypothesis tests, including the expression (the formula) for the test statistic in symbolic form and the expression with the values in the right places. The result can then be calculated by whatever method you like (TI-83, laptop computer, etc.). If more space is needed for a problem, continue your work on the back of the page.
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Final Exam
Statistics 300:Introduction to Probability and Statistics
Fall Semester 2011Cosumnes College
Instructor: L.C. Larsen
Instructions
Time: 2 hours and 5 minutes on 12/9,12/12, or 12/13.
Materials: Open book, notes, homework, etc.
Instruments: Calculator/Laptop of student's choice
No phones or consultantsExcept to call the instructor : 346-6324.
Answers to confidence interval problemsmust include the expression (the formula) in symbolic form and theexpression with all of the values inserted in the proper places. Then,the final answer can be calculated by any method or device.
Unless a p-value is given in the problem, each hypothesistest problem must include all four parts of the traditionalapproach to hypothesis tests, including the expression(the formula) for the test statistic in symbolic form and the expressionwith the values in the right places. The result can then be calculatedby whatever method you like (TI-83, laptop computer, etc.).
If more space is needed for a problem, continue your work on theback of the page.
Statistics 300Exam #3 Name:
Fall 2011Tue/Thu 7:00 - 9:05 pm
(9 points; 10 minutes)1. Use the row percentages in the table to test the idea that the percentage of Phoenix Suns fans
that live in California is the same as the percentage of Sacramento Kings fans that live inArizona.
Use a 5% significance level for this test.
The data represent truly randomsamples of Suns, Kings, and Sonicsfans.
FavoriteBasketball Team
Phoenix Suns
Sacramento Kings
Seattle Sonics
Home StateAZ
68%
21%
11%
CA
15%
68%
18%
WA
12%
7%
81%
RowTotal
190
191
219
Hn:
H,:
Statistics 300Exam #3 Name:
(8 points; 8 minutes)2. Is there a linear relationship between daily average
temperature and daily average wind speed? Use thedata in the table for a random sample of five daily valuesto test the claim that mean temperature and mean windspeed are negatively correlated. (Let a = 0.10 for this test.)
Claim:
Fall 2011Tue/Thu 7:00 - 9:05 pm
Day
12345
MeanTemp.
°F
91.981.493.270.8100
MeanSpeed
m/s
15.713.821.533.62.1
H0:
HI:
Statistics 300Exam #3 Name:
Fall 2011Tue/Thu 7:00 - 9:05 pm
(9 points; 10 minutes)3. Use the summary statistics for a random selection of Fridays and Saturdays to test the claim
that the average number of cars on a Sacramento freeway is at least 1000 more on Fridaysthan it is on Saturdays. (Use a 0.025 significance level for this test.) Differences in average trafficon Fridays are known to be larger than they are on Saturdays.
Hn:
HI:
Sample Statistic
N =
Average =
Standard Deviation =
Fridays
10
38,378
838
Saturdays
16
36,811
901
Statistics 300Exam #3 Name:
Fall 2011Tue/Thu 7:00 - 9:05 pm
(9 points; 10 minutes)4. Use the survey results given in this problem to test the claim that the proportion of prison
inmates who return to prison after being released is independent of the type of crime forwhich they were convicted. Use a Type I error rate of 0.05 for this test.
Type ofCrime
ViolentFelony
Non-violentFelony
ViolentMisdemeanor
Non-violentMisdemeanor
Returned to PrisonYes
35
26
31
32
No
65
74
69
68
Hn
Statistics 300Exam #3 Name:
Fall 2011Tue/Thu 7:00 - 9:05 pm
(13 points; 13 minutes)5. Daily air pollution measurements from communities that are near one another usually have
a linear relationship to one another. Use the data for Chico and for Yuba City to answer thequestions on this page and the next page.
Day
123456
YubaCity
758488574654
Chico
10396128755182
(a) Plot the points on the graph.
(b) Use your calculator todetermine the equation ofthe line that best predicts
Relationship of Daily Pollution at Two Cities
QD
QC
RD -
yc
* fbb 70
1 65m fifl
0 EC _
I 55= c/-\
Q./1C
4D
50 60 70 80 90 100 110 120 130
Pollution at Chico
pollution at Yuba City based on pollution at Chico.
equation =(c) Plot your line on the graph.
(d) What is the predicted pollution at Yuba City when pollution at Chico is 100?
(e) Estimate the correlation of pollution at Chico and Yuba City on all days?
(f) What proportion of the variation in pollution levels at Yuba City for thisset of six days is explained by the levels of pollution at Chico?
(g) For the "total" variation in the Yuba City pollution data:
The expression is: The value is:
(h) For the "explained" variation in the Yuba City pollution data:
The expression is: The value is:
(i) For the "unexplained" variation in the Yuba City pollution data:
The expression is: The value is:
Statistics 300 Fall 2011Exam #3 Name: _____-_^_——__-^__^__-—_ Tue/Thu 7:00 - 9:05 pm
(2 points; 2 minutes)6. Continue using the Chico and Yuba City pollution data to answer the questions below.
(a) For the "standard error of estimate" in relating Yuba City pollution to Chico pollution:
The expression is: The value is: ^___________
Statistics 300Exam #3 Name:
Fall 2011Tue/Thu 7:00 - 9:05 pm
(6 points; 6 minutes)8. Connect each picture with one of the candidate "r" values by writing the appropriate
candidate "r" value in the space at the top of each graph.
Candidate values of "r", the sample correlation coefficient.0.00 -0.70 -0.90 -1.00 0.70 0.90 1.00
-|C
in _
c
n
_5
i
•
11
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0 2 4 6 8 10
0 --2-4 --6 --8
-10 --12 -
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•• ,
D 2 4 6 8 10
20
-2-4-6-8
-10-12
1
•
l .
11 •i l •
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D 2 4 6 8 10
A -
9
n9
A -
et
I
0
l
1 •
2
l
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i
1 «
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4 6 8 10
0
9
1
n
-t
9
0
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11
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2
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1 • 1
4 6 8 10
20
-2-4-6-8
-10-12-14
ii
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— 11•
1
0 2 4 6 8 10
Statistics 300Exam #3 Name:
Fall 2011Tue/Thu 7:00 - 9:05 pm
(9 points; 9 minutes)9. Based on the statistics shown below, construct an 84% confidence interval for the difference
between the percentage of 15 year old girls that have a personal cell phone and the percentageof 15 year old boys that have a personal cell phone. (For the test, let a = 0.05.)
Sample Statistics
PersonalCell Phone
15 Year OldGirls Boys
Yes
No
90
45
51
41
Based on your interval is it reasonable to claim that the percentage of 15 year old boys that havea personal cell phone is greater than the percentage of 15 year old girls that have a personal cellphone?
Yes No Why?
Statistics 300Exam #3 Name:
Fall 2011Tue/Thu 7:00 - 9:05 pm
(9 points; 7 minutes)10. Use the information on this page to complete the Analysis of Variance table and test
the claim that milk from nine different producers has the same average "shelf life"(number of days before milk goes bad). Use a 10% significance level for the test.
AOV Table
Source SS
Producer
Error
Total
df MS p-value
9.818 0.0474
671.41
Hn:
H,:
Shelf Lives (in "days" ) of Milk samples from Nine Producers
A
15.611.114.716.218.214.815.314.514.316.313.818.811.612.612.510.5
n= 16x= 14.4s= 2.4
B
14.711.717.916.116.213.112.912.013.112.313.013.918.114.713.410.713.1
1713.92.1
C
17.213.514.114.213.917.114.014.917.215.413.218.213.918.714.0
1515.31.9
D
16.115.510.411.812.612.013.714.417.211.415.916.610.914.213.0
1513.72.2
E
14.516.014.913.917.114.113.815.217.816.3
1015.41.4
F
16.212.714.413.413.716.415.88.714.617.716.714.3
1214.62.4
G
14.111.716.614.410.411.910.914.310.314.112.712.912.47.312.213.318.0
1712.82.5
H
13.215.716.218.413.818.516.19.013.616.614.813.513.114.514.317.6
1614.92.4
I
17.614.012.512.715.812.612.013.714.812.616.517.610.916.1
1414.22.2
Statistics 300Exam #3 Name:
Fall 2011Tue/Thu 7:00 - 9:05 pm
(9 points; 10 minutes)11. Two programs for encouraging school attendance were studied at five schools. At each
shool, half of the students were randomly assigned to Method A and the other half wereassigned to Method B. Use the data below to prepare a 98% confidence interval for thedifference between the population means for the two methods.
1000's of Student-Daysof Attendance
School
12345
mean =
st. dev. =
Method A
70.474.964.380.876.3
73.3
6.27
Method B
69.478.968.383.878.3
75.7
6.65
Statistics 300Exam #3 Name:
Fall 2011Tue/Thu 7:00 - 9:05 pm
(8 points; 8 minutes)12. Five schools competed for best daily attendance. The competition lasted for 180 days.
Use the results below to test the claim that all of the schools were equally likely to winon each of the 180 days during the competition.(Let alpha be 0.025 for this test.)
School
A16Bi
tettl i
Countof Days
school won
3629
§?47
§1
1801 OU
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