Download Midterm Exam Part II

Midterm Exam Part I (2 questions – 20 points each)
NOTE: For the first two problems, you have to show all your work in order to get full
credit.
1.
(20 points) The following are Minitab outputs for the weight of 2000 college female students.
Descriptive Statistics: C1
Variable
C1
N
2000
Mean
125.00
Median
124.00
TrMean
124.66
Variable
C1
Minimum
71.40
Maximum
176.88
Q1
114.00
Q3
135.00
StDev
15.00
SE Mean
0.35
Histogram of C1, with Normal Curve
Frequency
150
100
50
0
80
130
180
C1
a) Find out the Five-Number-Summary statistic. (3 points)
b) What is the shape of the distribution of those female college students, how did you make your
judgment? (3 points)
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c) For this sample of weight of college females, what proportion weight less than 124.00 pounds? (4
points)
d) Between what 2 numbers would you expect 95% of the weight to lie? Also explain which rule you
need to use to solve this problem? (5 points)
e) Using the data above, what is the probability that we pick a female student at random and her weight is
between 110 pounds and 130 pounds? (5 points)
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2. (20 points) Suppose we try to find the relationship between genders and the number of tattoos that one
has. We use 0 to represent someone has no tattoos, 1 to represent someone has 1 tattoos, and 2 to
represent someone has 2 or more tattoos. The Minitab output is the following:
Tabulated Statistics: Gender, Tat_Cat
Rows: Gender
female
male
All
Columns: Tat_Cat
0
1
2+
All
222
130
352
31
20
51
4
7
11
257
157
414
Chi-Square = 3.273, DF = 2, P-Value = 0.195
1 cells with expected counts less than 5.0
Cell Contents -Count
a) What is the percentage of females who have no tattoos? (3 points)
b) Among those who have 1 tattoo, what percentage is male? (3 points)
c) Is there a statistically significant relationship between Gender and Tat_Cat? Explain how you
obtained this answer?
(4 points)
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d) What is the proportion of the males who have one tattoo (among all males)? Can we use the normal
approximation rule on the proportion distribution of males who have one tattoo? Explain your reason.
(5 points)
e) Suppose we can use the normal approximation rule, give a 98% confidence interval for the population
proportion. Note: for 98% confidence level, z* (the multiplier) is 2.33. (5 points)
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Midterm Exam Part II (20 questions – 3 points each)
Record your answers on the Scantron sheet.
Make sure you “blacken” out your ID # as well as your section number.
1. Which of the following is not a numerical summary of a dataset:
A. the sample mean
B. the sample median
C. the first quartile
D. the stem-and-leaf plot
E. the 95th percentile
2. A recent Gallup poll estimated that 70% of American adults are in favor of capital punishment. Which of
the following is a 95% confidence interval for the proportion of all American adults who are in favor of
capital punishment?
A. 0.6804 to 0.7196
B. 0.24 to 1.16
C. 0.67 to 0.73
D. cannot determine because we don’t know the sample size
3. Is the following statement TRUE or FALSE: The width of a confidence interval can be determined by
knowing only the confidence level.
A. True
B. False
4. Which one of the following samples sizes would make this statement TRUE: If the distribution of income
for PSU Alumni is skewed, the normal approximation curve for sample means can be used.
A. n=10
B. n=25
C. n=50
D. not enough information
5. If a conservative 95% confidence interval for the proportion of students who have MP3 players is 0.15 to
0.35 (15% to 35%) and this is based on a sample size of 100. What would the conservative 95%
confidence interval look like if the sample size has increased from 100 to 1000? (You do not need to
calculate anything. Think of how sample size is related to the confidence interval.)
A. .22 to .28
B. .10 to .40
C. 0.15 to 0.35
D. 0.00 to 1.00
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6. A recent poll reported that 20% of all college students have at least one tattoo. The 95% margin of error
for the poll was 3%. Which of the following statements is correct?
A. We can be certain that the percentage of all college students who have at least one tattoo is in
the interval 17% to 23%.
B. The chance is 95% that 20% of all college students have at least one tattoo.
C. With 95% confidence we can say that the percentage of all college students who have at least
one tattoo is between 17% and 23%.
D. The chance is 5% that 20% of all college students have at least one tattoo.
7. The primary purpose of a confidence interval is to __________.
A. describe how individuals within a population differ from the population average.
B. estimate a population parameter.
C. estimate a sample mean.
D. be confident that the population mean is a good estimate of the sample mean.
8. The ‘spread’ or ‘variability’ of data __________.
A. refers to how much the observations deviate from a normal distribution.
B. determines the 50th percentile of a distribution.
C. is measured using the mean or median of the data.
D. is measured using the standard deviation or the interquartile range.
9. The standard error of a proportion is given by which one of the following formulas:
p(1  p)
pˆ (1  pˆ )

s
A.
B.
C.
D.
n
n
n
n
10. A researcher conducts a study to determine whether or not smoking causes lung cancer. Which of the
following statements best reflects the variables in the study?
A. Lung cancer is the explanatory variable and smoking is the response.
B. Smoking is the explanatory variable and lung cancer is the response.
C. Lung cancer and smoking are both explanatory variables.
D. Lung cancer and smoking are both response variables.
11. The conservative margin of error for the proportion p̂ in a poll of 2,500 people is ___
A. 0.0004
B. 0.0008
C. 0.02
D. 0.04
12. A recent CNN Poll asked ‘Do you approve of the latest U.S. bombing attack on Iraq?” Yes___ No ___
Suppose that actually 60% of all adults in the U.S. would say ‘yes’ if asked. For a sample of size 600 let X
denote the number of people in the sample who say ‘yes’. The mean (expected value) and standard
deviation of X are ___
A. 60% and 12 B. 0.60 and 0.02
C. 360 and 12
D. 360 and 144
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Problems 13 and 14 refer to the following Minitab output:
Descriptive Statistics:
Variable
Data
N
100
Mean
18.00
Median
25.00
TrMean
24.50
Variable
Data
Minimum
20.00
Maximum
100.00
Q1
22.00
Q3
50.00
StDev
14.00
SE Mean
1.40
13. Which set of numerical measures of location and spread are most appropriate to use in this situation?
A. The mean and standard deviation
B. The median and standard deviation
C. The mean and interquartile range
D. The median and interquartile range
14. Which one of the following statements is not correct:
A. 50% of the observations are equal to or less than 25.
B. 50% of the observations are between 22 and 50.
C. 75% of the observations are equal to or greater than 25
D. 75% of the observations are between 22 and 100.
15. The width of a confidence interval for a proportion does not depend on one of the following: which one?
A. the value of the sample proportion, p̂
B. the confidence level
C. the sample size
D. the value of the population proportion, p
Problems 16 and 17 refer to the following: The time it takes to drive from State College to downtown
Philadelphia has a bell-shaped distribution with mean 220 minutes and standard deviation 20 minutes.
16. Between what two numbers of minutes do about 95% of drivers take to drive from State College to Philly?
A. 200 and 240 B. 180 and 260
C. 160 and 280 D. 150 and 250
17. Suppose we ask a random sample of 16 students how long it took them to drive to Philly. Between what
two numbers would you expect their average x to be with probability about 0.95?
A. 180 and 260 B. 200 and 240
C. 210 and 230 D. 215 and 225
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18. A sampling distribution is __________.
A. the probability distribution of a parameter.
B. the probability distribution of a statistic.
C. an unbiased estimate of the population mean.
D. an unbiased estimate of the sample mean.
19. A researcher wished to see if people could perform a task faster if they received positive feedback as they
did it. She randomly assigned 10 subjects to perform the task without feedback (Group 1) and 10 others to
do it with feedback (Group 2). The data collection method used in this study was a ______.
A. observational design.
B. randomized experiment.
C. matched-pair design.
20. A table is given below involving probabilities and a random variable X:
k
-----
0
0.05
1
0.15
2
0.30
3
0.40
4
0.05
5
0.05
A. The table is for a probability distribution function (PDF).
B. The table is for a cumulative probability distribution (CDF).
Formulas:
x = z + 
p̂  z*
=
s.d.( p̂ ) =
pˆ (1  pˆ )
n
 (x
i
)2
n 1
p(1  p)
n
1
n
E(X) = np
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
s.d.( x ) =
s=
s.d.(X) =
 (x
i
n
x)2
n 1
np(1  p)