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Unformatted text preview: Question Pnn
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N “1.2 Ill # 2 32 mmmm—mﬁ—mm—qH—mmmm—mm M_q—1m_~mmmhﬁm_ﬂw—qm—.ﬂ (A)
(B)
(C)
(D)
(E) (A)
(B)
(C)
(D)
(E) (A)
(B) (C)
(D)
(E) Practice Exam 1
Multiple Choice A concert hall has 2000 seats. There are 1200 seats on the main ﬂoor and 800 in the balcony.
40% of those in the balcony buy a souvenir program. 50% of those on the main ﬂoor buy a
souvenir program. At a certain performance all seats are occupied. If an audience member is
selected at random, what is the probability that a program was purchased? 22.5%
44%
45%
46%
92% Researchers conducted a 23 year study among 10,125 government employees in a certain
country. All were men over the age of 40, and eventually 369 died of strokes. Participants were
surveyed at the beginning about their perception of family problems. Among the 9000 who
reported a happy personal life, 3.5% died from strokes. Among the 1125 those who reported
serious problems in their personal life, the death rate from strokes was 4.8%. What is the pvalue
of the appropriate test to see if there is a relationship between personal happiness and death from
strokes? 0.028
0.031
0.042
0.062
0.083 A car dealer in a large city wants to estimate the proportion of pickup trucks compared to all
vehicles. He decides to take several random samples of size 100 from the parking lot at a
baseball stadium using the numbers that are already assigned to each stall. Which of the
following is NOT a correct statement? Because of sampling variability each sample could produce a different proportion The margin of error for a 90% conﬁdence interval is independent of the number of trucks in the
parking lot. The sample may be biased since baseball fans may not have the same preferences as the general
population. If a particular numbered stall selected at random does not have a truck, it is acceptable to
continue examining stalls to the left until a stall with a truck is found. It is improper to select the ﬁrst'100 stalls closest to the main gate, since those owners are likely
to have reserved parking which is an indication of income levels. (A)
(B)
(C)
(D)
(E) (A)
(B)
(C)
(D)
(E) (A)
(B)
(C)
(D)
(E) The mean score for a round of golf by Tiger Woods during the 1999 and 2000 seasons was 68.04
with a standard deviation of 2.4. Assuming that scores his scores remain independent and
normally distributed, what is the probability that he will shoot two consecutive scores of 66 or
less in the ﬁrture? ' 0.04
0.08
0.1 l
0.20
0.39 A spinner has an equal chance of landing on any one of the numbers 110. A student spins the
spinner 100 times and ﬁnds the total of the numbers. This is repeated 150 times. The results of
each trial are plotted in a histogram. Which of the following best describes the shape of the histogram? Approximately normally distributed with a mean of 550. Binomially distributed with a mean of 550. Uniformly distributed with a mean of 550. Continuously distributed with a mean of 550. Cannot be determined since the mean of the sample was not computed. Doctors believed that patients who received heart pacemakers seemed to snore less. Among 40 randomly selected patients with a pacemaker, 12 snored. Among 60 randomly selected patients without a pacemaker, 25 snored. Which of the following statements is NOT correct? I. The evidence supports the theory at the 10% level II. The 95% conﬁdence interval for the difference between the proportion of those who
snore in the two groups is (0.31, 0.07) 111. Since the conﬁdence interval contains 0, there is a signiﬁcant difference between the two
preportions. I Only 11 Only III only I and III I, II, and 1]] are incorrect .J‘ ._H.J .«_  ——J—. Mair—AA» H—«h—A—n—a—‘dgatw—JuﬂﬁLM M$WW 7. A strength coach wants to determine if there is a relationship between the weight of an individual
and how much weight they can lift. The data was collected and analyzed using a statistical soﬁwareprogramjheoutputisshnwnbelow. — StudentWeight _
TotaIWeighthed Underiso
43 7 87 Under 200 44
40.0 47.0 87.0
0.40 . 0.00 0 34
Over 200 ‘ 33 63
34.0 03.0
0.47 0.00
Total 09 01
69.0 81.0 The number of rows with at least one missing value is 0
ChiSquare Statistics Section Chisquare 1 .745200
Degrees of Freedom 1.0000
Probability level 0.18641
Phi .107864
Cramer’s V .107864
Kappa’s t value 1.32106
McNemar’s Probability Level .029049 Based on the information, which of the following is a correct statement? (A) Since the value of the xzstatistic is so small, there is a strong relationship between the weight of
an individual and the weight they can lift. (B) Since the value of the xzstatistic is so small, there is no evidence of a relationship between the
weight of an individual and the weight they can lift. (C) The correlation coefﬁcient of a linear regression equation would be less than 0.20. (D) The P—value of this test is 0.18641 which indicates no signiﬁcant relationship between the weight
of an individual and the weight they can lift. (E) The Pvalue of this test is 0.029049 which indicates a very strong relationship between the
weight of an individual and the weight they can lift. 8. (A)
(B)
(C)
(D)
(E) (A)
(B)
(C)
(D)
(E) The following is a stem and leaf plot for the number of defective chips in a batch of 300 chips for
two different machines. 99888
443333222222
8888777666666655555 57778899
001 124444
66777889
00001123
6688 , 0 1100 unnummma— 1 2l means 21 Based on the plot which of the following statements is True? The output from Machine B has more variability than that of Machine A
The mean from Machine A is greater than the mean from Machine B.
The data from Machine A has less skewness than from Machine B I only 11 only 111 only I and HI only All statements are true An author wrote a book that advocated the playing of classical music to little children. The author cited a study that reported that students who choose to play a musical instrument score an average of 51 points higher on the Scholastic Aptitude Test than students who do not play an instrument. Which of the following statements is not correct? I. There is a relationship between playing instruments and receiving a higher score on the
SAT. II. The study was observational rather than an experiment. 111. Playing a musical instrument will cause a student to score higher on the SAT IV. The study was a matched pairs study. IandII
HandIII
IandIV
HandIV
IIIandIV 10. (A)
(B)
(C)
(D)
(E) 11. (A)
(B)
(C)
(D)
(E) 12. (A)
(B)
(C) (D)
(E) 13. (A)
(B)
(C)
(D)
(E) Randomization is an important characteristic of a welldesigned experiment in order to eliminate
bias. Which of the following sources of bias is eliminated by randomization? Researchers have a desired outcome in mind. Certain groups from the population are systematically excluded ﬁ'om the data.
Certain groups from the population are categorically excluded from the data.
People with strong opinions are counted before others. Some groups are aware of the reason for the data search. A spinner on a full circle can take on any decimal value between 0 and 400. What is the
probability that the spinner will land between 175 and 225? 0.12 0.14 0.44 0.50 0.56 A poll of a random sample of 1068 people in Sweden (total population of 9 million) found that
about 75% favored government supported health care. A similar poll of 1068 people from
England (population 60 million) showed that about 75% favored government supported health
care. Which of the following statements is TRUE? Since the same number of people had the same opinions, the results are equally accurate.
Since the Swedish poll represented a larger proportion of the population, it is more accurate.
Since the population of England is larger, the English poll gives a better indication of the
opinions of the people. No decision can be made since the conﬁdence interval is not stated. No decision can be made since the populations are different and the standard deviations are
unknown According to the US Census, the proportion of adults in a certain county who owned their own
home was 0.71. A SRS of 100 adults in a certain section of the county found 65 owned their
homes. What is the probability of obtaining a sample of 100 adults in which 65 or fewer own
their own homes, assuming that this section of the county has the same overall proportion of
adults who own their homes as does the entire county? 0 0.093
0.106
0.186
0.907 14. After a snowstorm in a large metropolitan area, meteorologists took a random sample of several
locations and measured depth of the snow along with the water content. The results were
summarized in a comuter printout. Regressim Flt Y = ~3.0E02 4 0.103414X
RSquared = 0.950
K in a 95.0% Confidence Bands — 95.0% Bands w; LINEAR REGRESSION ANALYSIS
The regression equation is Water = 003039 + 0.10341*nches
R SQR = 0.95020 R = 0.97478
DF=4 T = 8.610 P = W Unfortunately, the printer failed just as the Pvalue was being displayed. What is the Pvalue for the
hypothesis test H0: [5 = 0 vs. H1: [3 #5 0? (A) P < 0.001 (B) P = 0.001 (C) P = 0.0304 (D) P = 0.103 (E) P = 0.950 15. The monthly power usage in a rural area is given by j) = 2. 7 + 1.01:: where j> is the number of kilowatts used and x represents the number of months since January I, 2000 (Let January 2000 correspond to x = 0). What is the estimated monthly power usage for December 2002?
(A) 5.73 kw (B) 25.93 kw
(C) 26.94 kw
(D) 38.05 kw
(E) 39.06 kw 16. (A)
(B)
(C)
(D)
(E) 17. (A)
(B)
(C)
(D)
(E) 18. Eight people who suffer from hay fever volunteer to test a new medication that will relieve the
symptoms. The names of the volunteers are l . Zavala 5. Harris
2. Liu 6. Elifritz
3. Lonnquist 7. Klein
4. McGarry 8. Scott Four of the volunteers will receive the new medication while the other four will receive a
placebo as part of a double blind experiment. Starting at the left of the list of random numbers
below and reading from left to right, assign four people to be given the medication. 07119 97336 71048 08178 77233 13916 47564 81056 97025 85977 29372
The four people assigned are Zavala, Liu, Lonnquist, Klein
Liu, Harris, Klein, Scott Zavala, Lonnquist, Elifritz, Klein
Zavala, Lonnquist, Klein, Scott
Zavala, McGarry, Klein, Scott A child is 40 inches tall which places her in the top 10% of all children of similar age. The mean
height for such children is 38 inches. Based on this information, what is the standard deviation? 0.20 inches
0.31 inches
0.65 inches
1.21 inches
1.56 inches A study was done to compare the effectiveness of two different groups of teachers. 15 different
measures were used. In all cases the mean scores of an SRS of the students of the teachers from
Group A were higher than the mean scores of an SRS of the students of the teachers in group B.
The report of the study stated that in 2 of the 15 measurements the sample size was too small to
verify that the difference was statistically signiﬁcant. This is an illustration of (A) Good replication
(B) Placebo effect (C) Low power (D) Stratiﬁed sampling
(E) Marginal frequency 19. (A) (B)
(C) (D)
(E) 20. (A)
(B)
(C)
(D) (E) 21. (A)
(B)
(C)
(D)
(E) 22. (A)
(B)
(C)
(D) (E) Trafﬁc engineers studied the trafﬁc patterns of two busy intersections on opposite sides of town
at rush hour. At the ﬁrst intersection, the average number of cars waiting to turn left was 17 with
a standard deviation of 4 cars. At the second intersection, there are 25 cars waiting to make a left
turn with a standard deviation of 7 cars. The report combined the mean number of car at both
intersections. Assuming the data are independent, the standard deviation of the sum is Jﬁ cars
mews
Scars J5me 11 cars A newspaper wants to know public opinion of a town regarding the construction of a new library
in a downtown location. It is decided that 48 peeple will be surveyed using a simple random
sample. Which of the following will produce a simple random sample. Record the opinion the ﬁrst 48 people who visits the newspaper's web site Survey every fourth person who enters the current library until 48 people have responded.
Randomly select 48 people from the city phone directory. Randomly select 12 people from each of the northwest, northeast, southwest, and southeast
sections of the city. Number the residents using the latest census data. Use a random number generator to pick 48 people. Suppose the probability that a soﬁball player gets a hit in any single atbat is .300. Assuming
that her chance of getting a hit is independent, what is the probability that she will not get a hit
until her fourth at bat in a game? 0.0081
0.1029
0.3430
0.41 16
0.7599 Which of the following statements is FALSE? The power of a hypothesis test increases as at increases. The power of a hypothesis test does not depend on the sample size. [3 is a measure of the probability of a Type [I error. The power of a hypothesis test is a measure of the ability of the test to detect a difference
between the estimated value and the true value of a parameter. As the ctlevel increases, the Blevel of a hypothesis test decreases. 10  A J“ a . r .41” A. “4.). —+——J u». r "gnu—4 mull—“J” wme 23. (A)
(B)
(C)
(D)
(E) 24. (A)
(B)
(C)
03)
(E) 25. (A)
(B)
(C) (D)
(E) 26. (A)
(B)
(C)
(D)
(E) The state Employment Service of a certain state certiﬁes the typing speed of applicants. Suppose
typing speeds are approximately normally distributed with a mean of 55 words per minute with a
standard deviation of 4 words per minute. If Kim scores at the 95‘'1 percentile, then her typing
speed is closest to 47 wpm
50 wpm
59 wpm
62 wpm
67 wpm A new dietary supplement was given to a volunteer group of 25 people who were at least 50
pounds overweight. 18 peOple from the group lost at least 20 pounds. What should we conclude
about the effectiveness of the diet? The diet waseffective in 72% of the cases. The mean weight loss was more than 20 pounds. Nothing, since the 25 people were not an SRS. Nothing, since there was no control group that received a placebo.
Nothing, since the group knew they were using the diet. A pharmaceutical company develops a new medication to lower a person’s cholesterol. The
advertisement for the new drug cites the results of an experiment comparing the drug with a
placebo stating the level had been lowered by an average of 13.2 mg/l with a P—value < 0.01.
Which of the following best explains the meaning of P—value? 1% of the people did better with the placebo than with the drug. Only 1% of the people experienced side effects. The probability is less than 1% of obtaining a difference in the mean cholesterol levels between
those taking the placebo and the those taking the medication is as large or larger than 13.2 mg/l if
the means for the placebo and medication groups were equal. All but 1% of the people on the drug experienced a drop of 13.2 mg/l. The difference between the two groups was not signiﬁcant. A linear regression was conducted on the following data points. A(l,11), B(3, 7), C6, 2),
D(7, 1), E(9, 2). The residual for which point has the largest absolute value? [TEUODIJ> 11 27. (A)
(B)
(C)
(D)
(E) 28. (A)
(B)
(C)
(D)
(E) Illlﬂﬂﬂﬂ Right hand nunnu Left An alumni association of a major university ﬁnds that 30% of their members attained advanced
degrees, 50% attained a bachelor’s degree and 20% did not graduate. The mean income of a
graduate with an advanced degree is $75,000, the mean income of a graduate with a bachelor’s
degree is $54,000, and the mean income of a nongraduate is $36,000. From past results, alumni
members donate 5% of their income to the university. If 50 members of the alumni association
are randomly selected, what is the expected total donation? $2,750
$2,835
$137,500
$135,000
$141,750 In order to determine the dexterity or handedness of people, 10 people were asked to roll a die
with one hand and make a tally mark with the other hand for 60 seconds. Then the subjects were
asked to use the other hand. The hand that each person used ﬁrst was decided by chance. The
number of tally marks made by each subject is shown in the table below. u One measure of handedness is the difference between the number of marks made by each hand.
What is the PValue for the appropriate hypothesis test? «0.910
0.376
0.493
0.715
0.754 12 29. A researcher made a scatter plot from some previously collected date; Thedata was clearly non
linear in shape. The researcher then tried a variety of transfonnationsen the data in an attempt
to linearize the results. The residue} plot for each transformation is shown below. Which of the transformations was best at linearizing the data? (A) #1
(B) #2
(C) #3
(D) #4
(E) #5 13 30. A spring is used to propel a toy rocket. In a sample of 10 toy rockets, the mean distance traveled
is 32.7 inches with a standard deviation of 4.3 inches. A stem plot reveals no evidence of non
normality. What is the 98% conﬁdence interval for the true mean of the distance traveled? (A) 32.7 s 3.16
as) 32.7 :I: 3.21
(C) 32.7 :I: 3.26
(D) 32.7 3: 3.76
(E) 32.7 s 3.34 31. A student is assigned a project in a statistics class. The student uses the Internet to ﬁnd the data
from the 2000 Census that lists the population for each state in the United States and computes
the 90% conﬁdence interval for the mean population of each state. The student’s statistics
teacher marks the answer wrong. Which of the following is the reason the student’s answer is
incorrect? (A) The data does not represent a true random sample.
(B) Since the data is highly skewed it violates the rules of thumb to construct a confidence interval. (C) A conﬁdence interval should never be constructed when population data is known.
(D) The degrees of freedom is unknown. (E) Using mean from each state to compute the overall mean is improper. 32. A survey of 259 families was made to determine if their vacation habits. The two way table
below shows the number of families by location (rural, suburban, urban) and length of most
recent vacation (1  7 days, 8 or more). Rural Suburban Urban 17 days 8 or more
days Total What is the probability that a randomly selected family was suburban given that they spent 8 or more
days on vacation? (A) 0.12
(B) 0.31
(C) 0.45
(D) 0.50
(E) 28.24 14 “any, Mm...) __AW‘W~*AHHHWM“J 4.3.. ... ‘ﬁ. 4 4‘1_’. K I ‘I M.“ 33. (A)
(B)
(C)
(D)
(E) 34. (A)
(B)
(C) (D) (E) A large bakery has a many different products for sale. Suppose that.70% of all customers of the
bakery order donuts, 50% order cinnamon rolls, and 40% order both. Ifa customer is randomly
selected, what is the probability that she ordered neither donuts nOr cinnamon rolls? 14%
20%
35%
48%
60% A group of eight people work on the ﬁfth ﬂoor of a building. They all decide they want to lose
weight by increasing their physical activity. Four of them decide to walk up the ﬁve ﬂights of
stairs each work day. The other four decide to walk down the ﬁve ﬂights at the end of the day.
They weigh themselves each Monday morning and report their weight to their supervisor. This
is an example of an experiment since they are divided into two equal groups. ‘ an observational study since the supervisor didn’t decide which group walked up the stairs.
block design since there are two treatments. 3 survey since the people volunteered to report their weight each week. an expianatory variable since they both increase their physical activity. 15 35. The histogram represents the yield (in bushelslacre) of 20 apple orchards in the northwest. The
class intervals are ;  ual. The ri t end int is included but the left endpoint is not. OAMU‘QOH. What proportion of orchards exceeded 60 bushels/acre? (A)
(B)
(C)
(D)
(E) 36. (A)
(B)
(C)
(D)
(E) 0.03
0.05
0.15
0.25
0.60 An advertisement for a diet supplement, LoozeNow, claims that it is scientiﬁcally proven that
LoozeNow will help people lose an average of 14.8 pounds in 30 days. The article further
explains that a double blind test was done to compare LoozeNow with a control group. The
mean weight loss of people on LoozeNow was 14.8 pounds with a standard deviation of 11.2
pounds. The mean weight loss of people in the control group was 15.1 pounds with a standard
deviation 12.5 pounds. Which of the following statements is true? LoozeNow caused people to lose weight.
The least amount of weight lost among the LoozeNow group was 3.6 pounds.
The weight loss among the LoozeNow sample was likely due to a placebo effect. The experiment wasn’t really double blind, since the people could tell if they were losing weight. Anyone who takes LoozeNow will experience a weight loss. 16 9. “NJ "k M.“ 37. (A)
(B)
(C)
(D)
(E) 38. “ 420.000 473.286 149.666 (83.431, 758.574) Automobile engineers checked the effect of a new automatic transmission on mileage. They
selected 50 cars of the same make and model. They randomly chose 25 of the cars to use the old
transmission while the other 25 cars received the new model of transmission. The mean of the
first group was 23.4 mpg with s = 3.4 mpg. The mean of the second gmup was 25.1 mpg with s
= 3.2 mpg. A hypothesis test on the difference between the means was conducted. Which of the
following is an assumption that allowed for the hypothesis test? The assignment of transmission was random. The sampling distribution of the difference between the sample means is bimodal.
Since the data was random, no linear regression was possible. The standard deviation of each group was different. The difference between the means was within a standard deviation. A study was done at a large midwestern university to determine if there was bias in the starting
salaries of short people when compared to people of above average height. Since the mean height
for women is different from the mean height for men, the researchers examined both men and
women. Graduates were selected from 5 different majors. For each major a randomly selected
woman at least 2 inches below the mean height for women was paired with a randomly selected
woman who was at least 2 inches above the mean height. Five pairs were similar selected from
males graduates from the same majors. The starting weekly salaries for each person in the pair
was recorded and the difference (Tall Salary— Short Salary) computed. The results were
summarized in the computer output below. Based on the data, which of the following statements is correct? (A)
(B) (C)
(D)
(E) A chisquared test should have been done since there were two factors  height and gender.
Since the conﬁdence interval did not contain 0, it is likely that the mean salary for tall people is
greater than the mean salary for short people. There is a 95% probability that the true mean difference in salaries lies between $83.43 and
$758.57. Since the conﬁdence interval was above 0, it is likely that the mean salary for tall people is
greater than the mean salary for short people. A sample size of 10 is too small to draw any conclusion. 17 39. The following graph represents the number of paid employees related to the 2002 Winter
Olympics from 1996 throu  . 2002 Winter Olympics Employment We mwnnmmm'm Which of the following statements are true? I. The data is skewed to the leﬁ. II. The data is skewed to the right. III. The mean number employed is about 5,000.
IV. The mean number is about 10,000. (A) I and III
(B) II and [[1
(C) I and IV
(D) II and IV (E) None of the above are true. 40. In a study children were asked to indicate which emotion they associated with the color blue.
The response and gender of the child are summarized in the table. . .
E
1? We wish to test the claim Ho: There is no relationship between gender and emotion vs. H,: There is a
relationship between gender and emotion. (Let a = 0.05) (A) Reject H0: If x2 = 0.103 (B) Reject Ho: If x2 = 6.17 (C) Reject H0: If x2 = 7.31 (D) Fail to reject Ho: If x2 = 14.07
(E) Fail to reject H0: If 12 = 15.51 .r_.L,_.L__.. J... 18 \ ...
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This note was uploaded on 08/27/2010 for the course MATH 1561 taught by Professor Ladwig during the Spring '10 term at Northwestern IA.
 Spring '10
 Ladwig
 Statistics

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