Statistics 108, Exam 1, Fall 2008
Name (print):_____________________
I confirm that I am allowed only a calculator and one 3-by-5 inch note card of notes for this
exam. I will not look at anybody else’s exam and I will take all necessary efforts to prevent
others from seeing my exam. The consequence of using additional test aids, copying from
others, or allowing others to copy my work will result in disciplinary action.
I have read and agree with the above statement. Signature: _____________________
1. 4pts. Answer:_____________. Using the values 𝑥1 = 2, 𝑥2 = 8, and
𝑦1 = 3, 𝑦2 = 1, calculate ∑ 𝑦𝑖 (𝑥𝑖 − 𝑥̅ )2 . Show your work.
For the following blanks, fill in whether the random variable is
nominal, ordinal, continuous or discrete.
2. 1pt. Answer:_____________ The brand of automobile (Toyota, Ford, etc.)
3. 1pt.Answer: _____________ Amount of pain after surgery (None, Some, Much)
4. 1pt.Answer: _____________ Semester grade in a class (A,B,C,D,F)
5. 1pt.Answer: ______________ Number of typographical errors in a page (0, 1, 2, etc.)
Circle whether the item is a parameter or a statistic.
6. 1pt. statistic
parameter: The mean weight of all 18 year old white men in America.
7. 1pt. statistic
parameter: The mean height of the 29 males in this class.
8. 1pt. statistic
parameter: The probability of a coin toss being heads.
The below steam-and-leaf plot shows the body temperature (in Fahrenheit) of 104 students.
Leaf Unit = 0.10
2
94
66
4
95
12
6
95
69
10
96
1334
17
96
6778999
33
97
0000011122233344
50
97
55566777888888999
(23) 98
00000001111111222233344
31
98
5555556666777889
15
99
0022233444
5
99
57
3
100 4
2
100 5
1
101 4
9. 2pts.Answer: ______________ How many students had body temperatures of 98.6 degrees?
Name:_______________
Boxplot of EurekaPrecip, LAPrecip
80
70
60
Data
50
40
30
20
10
0
EurekaPrecip
LAPrecip
The above boxplot graph shows 101 years of precipitation (rain in inches) data for Eureka and
Los Angeles.
10. 2pts.Answer:__________________ What is the approximate median rainfall for Eureka?
11. 2pts.Answer:__________________ Which city has the greatest range?
12. 2pts.Answer: __________________ Showing your calculations, give an estimate for the
interquartile range for Eureka.
\
13. 3pts. Answer:________________El Nino years are when the water near the equator is far
above normal. La Nina years are when the water near the equator is far below normal.
Neutral years are when the water temperature is intermediate. Over a 101 year period, 33
years were classified as being El Nino years, 23 years as La Nina, and 45 years as neutral.
If a pie chart were to be drawn, how many degrees would the La Nina slice require? Show
your calculations.
14. 2 pts. A study was performed to investigate how many miles Americans drive on a typical
week day. Researchers performed a telephone survey where, on a Wednesday, they asked
200 men and 200 women about how many miles they had driven on the previous Tuesday.
50 of the 400 people were randomly selected from rural areas and the remaining people were
from urban areas. Circle which of the following sampling methods was used:
(A) Systematic Sampling (B) Stratified Sampling.
2
Name:_______________
15. Using the six data values: 3, 8, 6, 4, 3, 0, calculate: (show your work)
a. 4pts. Mean =
b. 3pts. Median =
c. 2pts. Mode =
Scatterplot of Age vs Height
55
50
45
Age
40
35
30
25
20
1450
1500
1550
Height
1600
1650
16. 2pts. Which number is the closest to the sample correlation between Age and height?
(i) -35 (ii) -1 (iii) -0.8 (iv) 0 (v) +0.8 (vi) +1 (vii) +35
17. 2pts. Suppose the odds are 2:3 that you will win a game. What is the probability that you
will win the game?
18. Suppose a jar contains 3 black marbles and 3 white marbles. Suppose 2 marbles are
randomly sampled from the jar without replacement. What is the probability of getting 1
white and 1 black marble? Show your work.
3
Name:_______________
Scatterplot of Price vs Salary
120
110
100
Price
90
80
70
60
50
40
30
0
20
40
60
80
100
Salary
Price = 42.6 + 0.694 Salary
The above graph shows the relationship between average working salary and cost of living (Price)
for 46 major cities around the world. The salaries and cost of living are scaled to where Zurich,
Switzerland is 100 for both cost of living and salary. The equation for the regression line is given
below the graph.
Madrid, Spain had a salary level of 50 and a Price of 93.8.
19. 3pts. Calculate the regression line’s predicted Price for Madrid.
20. 2pts. Calculate the residual value for Madrid.
21. 2pts. For the Price vs. Salary scatter plot, circle the number that is closest to the correlation is:
(i) -42.6 (ii) -1 (iii) -0.8 (iv) 0 (v) +0.8 (vi) +1 (vii) +42.6
4
Name:_______________
The below table shows the counts of left-handed and right-handed students and their eye colors.
Tabulated statistics: eyes, hand
Rows: eyes
blue
brown
green
All
Columns: hand
left
right
All
2
5
3
10
23
22
12
57
25
27
15
67
Cell Contents:
Count
22. 3pts. Use the table to estimate 𝑃(𝑏𝑟𝑜𝑤𝑛 𝑒𝑦𝑒𝑠)=
23. 3pts. Use the table to estimate 𝑃(𝑏𝑟𝑜𝑤𝑛 𝑒𝑦𝑒𝑠 |𝑙𝑒𝑓𝑡 ℎ𝑎𝑛𝑑𝑒𝑑) =
Histogram of LAPrecip
25
Frequency
20
15
10
5
0
5
10
15
20
LAPrecip
25
30
35
24. 2pts. The above histogram shows precipitation amounts (inches) in Los Angeles for 101
years. The median precipitation was 13.5 inches. Compared to the median of 13.5 inches,
the mean is: circle (a) more, (b) less, or (c) about the same?
5
Name:_______________
25. 2pts. In the above Venn Diagram, shade in the region represented by 𝐴̅ ∩ 𝐵̅
26. 2pts. In the above Venn Diagram, shade in the region represented by𝐴̅ ∪ 𝐵̅.
6